%!PS-Adobe-2.0 %%Creator: dvips(k) 5.991 Copyright 2011 Radical Eye Software %%Title: arXiv:1210.1433v1 [cs.LO] 4 Oct 2012 %%CreationDate: Wed Mar 14 22:32:10 2018 %%Pages: 28 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentPaperSizes: Letter %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R2 -P pk -z relation_lifting_arxiv.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2018.03.14:2232 %%BeginProcSet: texc.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro 0 0 %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def @MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N} N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{ pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: color.pro 0 0 %! TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet %%BeginProcSet: hps.pro 0 0 %! /HPSdict 20 dict dup begin/braindeaddistill 50 def/rfch{dup length 1 sub 1 exch getinterval}bind def/splituri{dup(#)search{exch pop}{()exch} ifelse dup(file:)anchorsearch{pop exch pop 3 -1 roll pop false}{pop 3 -1 roll exch pop true}ifelse}bind def/lookuptarget{exch rfch dup /TargetAnchors where{pop TargetAnchors dup 3 -1 roll known{exch get true }{pop(target unknown:)print == false}ifelse}{pop pop (target dictionary unknown\012)print false}ifelse}bind def/savecount 0 def/stackstopped{count counttomark sub/savecount exch store stopped count savecount sub 1 sub dup 0 gt{{exch pop}repeat}{pop}ifelse}bind def /tempstring 128 string def/targetvalidate{1 index dup length 127 gt exch tempstring cvs dup(/)search{pop pop pop exch pop true exch}{pop}ifelse token{pop length 0 ne}{true}ifelse or not}bind def/targetdump-hook where {pop}{/targetdump-hook{dup mark exch gsave initmat setmatrix{{mark/Dest 4 2 roll targetvalidate{aload pop exch pop/Page 3 1 roll/View exch[exch /FitH exch]/DEST pdfmark}{cleartomark}ifelse}forall}stackstopped pop grestore}bind def}ifelse/baseurl{mark exch 1 dict dup 3 -1 roll/Base exch put/URI exch/DOCVIEW{pdfmark}stackstopped pop}bind def /externalhack systemdict/PDF known def/oldstyle true def/initmat matrix currentmatrix def/actiondict 2 dict dup/Subtype/URI put def /weblinkhandler{dup 3 1 roll mark 4 1 roll/Title 4 1 roll splituri 3 -1 roll dup length 0 gt{cvn/Dest exch 4 2 roll}{pop}ifelse{externalhack{ /HTTPFile exch}{actiondict dup 3 -1 roll/URI exch put/Action exch} ifelse}{externalhack{/HTTPFile exch}{/File exch/Action/GoToR}ifelse} ifelse counttomark 2 sub -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll /Color exch oldstyle{/LNK}{/Subtype/Link/ANN}ifelse gsave initmat setmatrix{pdfmark}stackstopped grestore}bind def/externalhandler where{ pop}{/externalhandler{2 copy{weblinkhandler}exec{/externalhack externalhack not store 2 copy{weblinkhandler}exec{/externalhack externalhack not store/oldstyle false store 2 copy{weblinkhandler}exec{ (WARNING: external refs disabled\012)print/externalhandler{pop pop}bind store externalhandler}{pop pop}ifelse}{pop pop/externalhack externalhack not store}ifelse}{pop pop/externalhandler{weblinkhandler pop}bind store} ifelse}bind def}ifelse/pdfmnew{dup type/stringtype eq{externalhandler}{ exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll/Color exch/LNK gsave initmat setmatrix pdfmark grestore}{pop pop}ifelse}ifelse}bind def/pdfmold{dup type/stringtype eq{externalhandler}{exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop pop 0 3 getinterval /Rect 3 1 roll/Border exch/LNK gsave initmat setmatrix pdfmark grestore} {pop pop}ifelse}ifelse}bind def/pdfm where{pop}{/pdfm /currentdistillerparams where{pop currentdistillerparams dup /CoreDistVersion known{/CoreDistVersion get}{0}ifelse dup braindeaddistill le{(WARNING: switching to old pdfm because version =) print ==/pdfmold}{pop/pdfmnew}ifelse load}{/pdfmark where{pop{dup type /stringtype eq{externalhandler}{2 copy mark 3 1 roll{pdfmnew} stackstopped{2 copy mark 3 1 roll{pdfmold}stackstopped{ (WARNING: pdfm disabled\012)print/pdfm{pop pop}store}{ (WARNING: new pdfm failed, switching to old pdfm\012)print/pdfm/pdfmold load store}ifelse}{/pdfm/pdfmnew load store}ifelse pop pop}ifelse}}{{ pop pop}}ifelse}ifelse bind def}ifelse end def %%EndProcSet TeXDict begin @defspecial systemdict /pdfmark known{userdict /?pdfmark systemdict /exec get put}{userdict /?pdfmark systemdict /pop get put userdict /pdfmark systemdict /cleartomark get put}ifelse /DvipsToPDF{72.27 mul Resolution div} def/PDFToDvips{72.27 div Resolution mul} def/BPToDvips{72 div Resolution mul}def/BorderArrayPatch{[exch{dup dup type/integertype eq exch type/realtype eq or{BPToDvips}if}forall]}def/HyperBorder {1 PDFToDvips} def/H.V {pdf@hoff pdf@voff null} def/H.B {/Rect[pdf@llx pdf@lly pdf@urx pdf@ury]} def/H.S {currentpoint HyperBorder add /pdf@lly exch def dup DvipsToPDF 72 add /pdf@hoff exch def HyperBorder sub /pdf@llx exch def} def/H.L {2 sub dup/HyperBasePt exch def PDFToDvips /HyperBaseDvips exch def currentpoint HyperBaseDvips sub /pdf@ury exch def/pdf@urx exch def} def/H.A {H.L currentpoint exch pop vsize 72 sub exch DvipsToPDF HyperBasePt sub sub /pdf@voff exch def} def/H.R {currentpoint HyperBorder sub /pdf@ury exch def HyperBorder add /pdf@urx exch def currentpoint exch pop vsize 72 sub exch DvipsToPDF sub /pdf@voff exch def} def @fedspecial end TeXDict begin 40258437 52099151 1000 600 600 (relation_lifting_arxiv.dvi) @start %DVIPSBitmapFont: Fa cmtt10 10 22 /Fa 22 118 df<007FB6FCA2B71280A26C1500A221067B9B2C>45 D<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B708A2C>I<15075DED1F80A2 153F16005D157E15FE5D14015D14035DA214075D140F5D141F5D143F92C7FC5C147E14FE 5CA213015C13035C13075C130F5C131F5CA2133F91C8FC5B137E13FE5B12015B12035B12 075BA2120F5B121F5B123F90C9FC5A127E12FE5AA21278A221417BB92C>I<121FEA3F80 EA7FC0EAFFE0A5EA7FC0EA3F80EA1F00C7FCAE121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F 80EA1F000B2470A32C>58 D<02FF13700107EBE0F84913F1013F13FF5B90B6FC4813C148 EB003F01FC131F4848130F485A491307121F5B003F14035B127F90C7FCED01F092C7FC5A 5AAB7E7EA2ED01F06DEB03F8123F7F121F6D1307000F15F07F6C6C130F6C6CEB1FE001FF EB3FC06C9038C0FF806C90B5FC6D14006D13FC010F5B6D13E0010090C7FC25357DB32C> 67 D<007FB512FCB612FEA46C14FC39000FE000B3B3A3007FB512FCB612FEA46C14FC1F 337AB22C>73 D<3801FFF0000713FE486D7E48804880819038C01FF8391F8007FC380F00 01000680C8FCA2140FEB07FF137F48B5FC12075A4813F8383FFC00EA7FE0EAFF8090C7FC 5AA36C1301A2387F8007383FE03F90B612FC6C15FE7E6C143F0001EBFC1F3A007FC00FFC 27247CA32C>97 D<903803FFF0011F13FC017F7F90B6FC4815805A48EB007FD80FF8EB3F 00D81FE0131E4848130C4990C7FC127F90C9FCA25A5AA67E7EA26DEB0F806C6CEB1FC07F 6C6C133FD80FFCEB7F803907FF81FF6C90B512006C5C6C5C6D5B011F13E0010390C7FC22 247BA32C>99 D<EC07FF4A13805CA28080EC003FA9EB0FF8EB3FFE90B512BF4814FF5A5A 380FFC0F381FF00349C6FC4848137F485A153F90C7FC5A5AA87E6C147FA26D13FF6C7E5C 381FF007380FFC1F6CB612FC6C15FE6CECBFFF6C143FD97FFC13FE90390FF01FFC28337D B22C>I<EB03FE90381FFFC0017F13F090B57E488048803907FE03FF260FF8001380D81F E0137F4848EB3FC049131F127F90C713E0150FB7FCA516C048C9FC7E7E7FED07C06C6CEB 0FE07F6C6C131FD80FFCEB3FC03907FF80FF6C90B512806C15006C5C013F13F8010F5B01 01138023247CA32C>I<EC07F8EC3FFCECFFFE497F4914805B90380FF87F9138E03F0001 1F131E4AC7FCA6003FB512FE4880B7FCA36C5C26001FC0C7FCB3A6007FB512F0B67EA46C 5C21337DB22C>I<ED03F0903907F81FFC90391FFE3FFE017FB5FC90B7FC5A48ECFE7F3A 07FE1FF87ED9F003133C000FECFC00EBE001001F80EBC000A5EBE001000F5CEBF0030007 5CEBFE1F90B55A5D485C5DD9DFFEC7FCEBC7F801C0C8FCA27F6CB512E015FE6CECFF8000 0F15C04815E04815F09039C0003FF848C7EA03FC007E140000FE15FE48157EA46C15FE00 7E15FCD87F801303D83FE0EB0FF8D81FFEEBFFF06CB612E06C15C06C1580C6ECFE00013F 13F80103138028387EA42C>I<EA3FF8487E12FFA2127F123F1201A9EC07F8EC3FFE91B5 FC01FD8090B67E82ECF81F9138C00FF0EC800714005BA35BB13B3FFFE03FFF80486D4813 C0B56CB512E0A26C496C13C06C496C13802B3380B22C>I<EB0380497E497E497EA36D5A 6D5A6D5A90C8FCA7383FFFE0487FB5FCA27E7EEA0007B3A6007FB512FCB612FE15FFA215 FE6C14FC20347AB32C>I<3A3FC1F803F03A7FE7FC0FF8B538FE3FFC6E487E6C91B5FC7E 3B07FE1FFC3F8001FC13F89039F80FF01F01F013E0A301E013C0B2D83FFC01F813F03B7F FE1FFC3FF8B5393FFE7FFCA23B7FFE1FFC3FF83B3FFC0FF81FF02E2481A32C>109 D<393FF807F8397FFC3FFE00FF90B5FC01FD806CB67E6C810001EBF81F9138C00FF0EC80 0714005BA35BB13B3FFFE03FFF80486D4813C0B56CB512E0A26C496C13C06C496C13802B 2480A32C>I<393FF80FF0397FFC7FFED8FFFDB5FC90B612806C15C06C15E000019038F0 3FF09138C00FF891380003FC5BED01FE491300A216FF167FA816FF6D14FE15017FED03FC 91388007F8ECC00F9138F03FF091B512E016C001FD148001FC1400EC7FFCEC0FF091C8FC AC383FFFE0487FB57EA26C5B6C5B283680A32C>112 D<903907F80F8090393FFF1FC049 139F48B512DF4814FF5A380FFE07381FF801EBE0004848137F5B007F143F90C7FC151F5A 5AA77E6C143F7F157F6C7E6C6C13FFEBF003380FFC0F6CB6FC7E6C14DF6C149F90383FFE 1FEB0FF890C7FCAC0207B5FC4A1480A46E140029367DA32C>I<D83FFFEB3FC048903881 FFE0B5008713F0028F13F86C019F13FC6C13BF39003FFFE3ED01F89138FC00F04A13604A 1300A25CA25CA35CAD003FB512F04880B6FCA27E6C5C26247EA32C>I<90383FF8700003 B512F85A5A5A5A387FC01F38FF000700FC1303A36CEB01F06C6CC7FCEA7FFC383FFFF06C 13FF6C14C06C14E0C614F0010F13F89038007FFCEC03FE003CEB00FF007E143F12FE7EA2 6D137F6D13FEEBF00790B512FC15F815F015E000F8148039701FFC0020247AA32C>I<13 0F497E133FA8003FB6FC481580B7FCA36C150026003F80C7FCAFED0380ED07C0ED0FE0A3 151F02C013C0011F133F9138F07F806DB5FC16006D5B6D13F801005BEC3FC0232E7EAD2C >I<D83FF8EBFFE0486C487F00FF5BA2007F7F003F7F00011407B3A2150FA2153F01FF13 FF6C90B6128017C06D15E07F6D01E713C00103010313802B2480A32C>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb rsfs10 8 1 /Fb 1 89 df<DB0FE0EC1FC0DB3FFCEC7FE0DBF03EEB01EF912603800FEB038FDA070090 3980060FC0021C010790381C0700DA380C6D48C7FCDA700E5C02E015C0EFC180902601C0 1E01C3C8FCD9038014C60200EB0FCE49013C13DC010615F8010E49485A010C5D4B485A90 261C01E05B913803C07F4A4848C9FC90390E1E00FE903907FC01FC903A03E01FFFE090C7 5A5FDB0FE0C9FCA24B5A153F5E4BCAFC5D4A5AA2020315E0DA07EC495A001FEB0FDC48D9 1F9C495A48021C49C8FC023E140E00FC01785C00E001F05C902603E00E5B26F007805C3B 7C1F00078380D83FFC6DB4C9FCD80FE0EB00FC433079AE3F>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmmi8 8 5 /Fc 5 122 df<15061507150EA45DA45DA45DA2D801F0140E486C141FD80FFC9038E03F 80EA1E3ED81C3F15C012380070903801C01FEE0F80017E140712E0EC0380EA40FC000016 00EA01F8EC07005ED803F0140EA2020E5B163C16385E4A5B15014B5AD801F8495A2700FC 381EC7FC90387FB8FC6DB45A010F13E0010190C8FCEB0070A35CA4495AA4495A13012A3C 7EAD2E>32 D<ED1F800003EC7FE048ECFFF04A13F8000E5B48903807E0FC91380F803C48 90380E001C5C4849131EA24A131C5A5CA25C01011438A24A1370010314F000F0EC01E0ED 03C0D87807EB0780007E9038001F00D83F87137E391FFF03FC6CEBFFF86C5C000114C06C 6C90C7FCEB1FF8013EC8FCA35BA313FCA3485AA25B6C5A272C7C9D2E>39 D<123C127EB4FCA21380A2127F123F1203A312071300A2120EA25A123C12385A12200915 7A8714>59 D<013F137C9038FFC1FE48EBE3FF3A03C1F787803A0701FE07C0D80E00130F ECFC1F5AD901F8138000381500150E001091C7FCC6485AA4495AA31503391C0FC007123E 127F150ED8FE1F131E00FC141CD8783F5B903873E0F0393FE1FFE0D81FC05B260F803FC7 FC221F7E9D28>120 D<EA03E0486C131C486C133ED81C7C133FD8387E137EA21270A248 4813FCA3EA41F80001EB01F8EA03F0A33907E003F0A4390FC007E0A40007EB0FC0141FEB E03F3803F0FF6CB512806C13DFEB3F1F1300EC3F00120E001F137E5A485B5C387E01F038 7C03E0383C0FC0D81FFFC7FC6C5AEA03F0202C7E9D23>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd msam10 8 1 /Fd 1 14 df<38600180EAE003B3A291B512FEA30280C7FCB3A3EA6001272E7CAD30>13 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe rsfs5 6 1 /Fe 1 89 df<DA07F8EC3F80DA3FFFECFFC0913AF80F80038F903C01C003C0070F809028 070001E00C1300D90E03D9F038C7FC011C01815B013801805BD97007EBF1C0923881F380 01E002F7C8FC91380F01FE5E9039C01E03F8D9E03C5B9038F07807D97FE05B90391F81FF FCEB0003A2DA003FC9FC157EA25D14014A5A14074B130E001C010F5C003ED91F70131800 7E013C5C4801785C27F001F0385B26E003C0EB038028780F001E0FC8FCD83FFCEB0FFCD8 0FF0EB03F03A2576A340>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmr6 6 1 /Ff 1 50 df<137013F0120712FFA212F91201B3A6B512E0A313217AA01E>49 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmss12 14.4 5 /Fg 5 115 df<B712E016FEEEFFC017F08317FE8301E0C780040F7F04037F04007F717E 717E171F717E17078483A21980A283A65FA21900A25F60170F4D5A173F4D5A4D5A160304 0F5B93B55A90B85A4DC7FC5F17F05F94C8FC16F801E0CBFCB3B1395376D24A>80 D<B712E016FEEEFFC017F017FC17FF8401E0C76C13E004077F04017F706C7E171F717E71 7EA271138083A219C083A65F1980A25F4D1300A24D5A171FEF7FFC4C485A04075B047F5B 90B85A6095C7FC17FC17F017C04CC8FCA29038E000078281836F7F8183167F83163F8370 7E160F83160783707FA2707F8284177F84717EA2717EA2717E170784711380A27113C0A2 7113E0F07FF0A2F03FF83D5376D24B>82 D<EC0FF891B5FC010314C0010F14F049804980 498090B7FC48EBF80F48D9C003138048497E91C7EA7FC0485A4848EC3FE049141F5B003F ED0FF05B127F16074915F890B7FCB8FCA60180C9FCA47FA2127FA27F123F7FA26C7EA26C 6C15206D15E06C6C14016C01C013076EEB3FF06C9038FC01FF6C90B6FC7F6D15E0010F15 806D1500010114FC6D6C13E0DA07FEC7FC2D387DB634>101 D<EAFFC0B3B3B3B3AB0A53 78D21B>108 D<39FF8001F0140F143F14FF13811387138F139FA29038BFFE00EBFFF05C 148091C7FC5B5B5BA25BA25BA35BB3AD1C3677B528>114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmsy10 14.4 2 /Fh 2 34 df<007FBA12FEBCFCA36C19FE4805769F5D>0 D<1B1EA21B1FA4757EA3757E A2757EA2757EA2757E881C7C1C7E88767E767E767E89767EF401FEF4007FF53FC0F51FF0 007FBE12FCC01280A36CF5FC00D0EA1FF0F53FC053C7FCF401FEF403F8525A65525A525A 52C8FC1C7E1C7C1CFC64515AA2515AA2515AA2515AA351C9FCA41B1EA2693F79BC78>33 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmr12 14.4 3 /Fi 3 59 df<15E01401EC03C0EC0780EC0F00141E5C5C14F85C495A1303495A5C130F49 C7FCA2133EA25BA25BA212015B1203A25B1207A25B120FA3485AA4123F90C8FCA45AA312 7EA412FEB3A3127EA4127FA37EA47F121FA46C7EA312077FA212037FA212017F1200A213 7CA27FA27FA26D7E1307806D7E13016D7E801478808080EC0780EC03C0EC01E014001B79 74D92E>40 D<12C07E7E12787E7E7E6C7E7F12036C7E7F6C7E1378137C7FA27FA26D7EA2 6D7EA280130380A2130180A2130080A3147EA4147F80A41580A3141FA415C0B3A31580A4 143FA31500A45C147EA45CA35C1301A25C1303A25C13075CA2495AA249C7FCA2133EA25B 137813F8485A5B485A12075B48C8FC121E5A5A5A5A5A1A7979D92E>I<120FEA3FC0EA7F E0A2EAFFF0A4EA7FE0A2EA3FC0EA0F00C7FCB3A9120FEA3FC0EA7FE0A2EAFFF0A4EA7FE0 A2EA3FC0EA0F000C3376B221>58 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj xycirc10 10 8 /Fj 8 72 df<126012F0AA1270A21278A51238123CA3121C121EA37EA36C7EA36C7EA27F 1201A26C7EA21378A27F133E131E131F7F806D7E1303806D7E130080147C8080EC0F80A2 EC07C0EC03E0EC01F0140015601C3F828118>64 D<126012F07E127E7E6C7E6C7E6C7EEA 01F86C7E137F6D7EEB0FE0EB07F8EB01FC6DB4FCEC3FC0EC0FF8EC03FE913800FFC0ED3F F8ED0FFF030113F09239003FFFC00407EBFFFCDC007F13FE17079438000FFC3F1C82463B >I<190C191E193E19FCF001F8F003F0F007E0F00FC0F03F00187E4D5A4D5AEF0FE0EF3F C04DC7FCEE01FEEE07F8EE3FE0EEFF80DB07FEC8FCED3FF8913801FFE0021F90C9FC9038 07FFF8007FB512C0B500FCCAFC14C0D87FE0CBFC3F1C82463B>I<156015F0AA15E0A214 01A515C01403A315801407A3EC0F00A3141EA35CA2147C1478A25CA2495AA2495A13075C 130F91C7FC5B133E133C137C5B5B1201485A485A485A48C8FCA2123E5A5A5A12601C3F82 8118>I<126012F07E127C7E7EA26C7E6C7E6C7E6C7E12007F137C133C133E7F7F801307 8013036D7EA26D7EA21478A2147C143CA280A380A3EC0780A3140315C0A3140115E0A514 00A215F0AA15601C3F82BC18>I<EA7FE0B512C014FC6CEBFFC0D8000713F89038001FFF 020113E09138003FF8ED07FE923800FF80EE3FE0EE07F8EE01FEEE007FEF3FC0EF0FE0EF 03F8717EEF007E84F00FC0F007E0F003F0F001F8F000FC193E191E190C3F1C82D43B>I< F00FFC943807FFFE177F0407B512FC043FEBC000922601FFF0C7FC030F90C8FCED3FF8ED FFC0DA03FEC9FCEC0FF8EC3FC002FFCAFCEB01FCEB07F8EB0FE0EB3F8049CBFC13FC485A EA07E0485A485A48CCFC127E12F85A12603F1C82D43B>I<156015F01401EC03E0EC07C0 EC0F80A2EC1F00143E5C5C5C1301495A5C1307495A91C7FC5B131E133E133C5BA25BA248 5AA212035BA2485AA348C8FCA3121EA3121C123CA312381278A51270A212F0AA12601C3F 82BC18>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk xybsql10 10 2 /Fk 2 112 df<0060140300F0EC07806C140F007EEC3F006C6C13FE391FF007FC0007B5 12F0000114C06C6C90C7FCEB0FF8210A828100>47 D<EB0FF8EB7FFF48B512C0000714F0 391FF007FC393F8000FE007EC7123F00F8EC0F804814070060EC0300210A9F8700>111 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmr5 5 3 /Fl 3 51 df<EA01FCEA07FF380F0780381E03C0383C01E0A2387800F0A300F813F8AB00 7813F0A3383C01E0A2381E03C0380F07803807FF00EA01FC151D7D9B1C>48 D<1360EA01E0120F12FFA212F11201B3387FFF80A3111C7B9B1C>I<EA03FCEA0FFF003F 13C038781FE0EB07F0EAFC0114F8A213001278EA000114F0A2EB03E0EB07C0EB0F80EB1E 005B1370EA01C038038018EA0700120C00381338387FFFF0B5FCA3151C7D9B1C>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmti7 5 2 /Fm 2 113 df<13F8EA03FEEA0707000E1380EA1C031238007813C0A238F00780A31400 5B130EEA701CEA7878EA3FF0EA0F8012127A9119>111 D<380783C0380FCFE03819FC70 3818F038EA31E0143C1201A23803C078A31470380780F014E0EB81C0EBC380380F7F0013 3C90C7FCA2121EA4EAFFC05B161A7E9119>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn bbold7 7 3 /Fn 3 122 df<EB1FE0EBFFFC4813FF00071480390FE07FC0391F807BE0393E0079F000 3C1378481478A25AA21260C7FC15F0147915E0EC7FC0A21580ECFE00EB03FCEB0FF0EB3F C001FFC7FCEA03FCEA07F0EA0FC048C8FC123E123C5AA25AB612F015F8A26C14F01D267D A524>50 D<EA7FE0487EA312F0B3AEB612FE15FFA26C14FE20287BA727>76 D<397FE0018039FFF003C0A2397FF80780EA7878393C3C0F00A2381E1E1EA26C6C5AA238 0787F813C73803C3F06C6C5AA23800F3C0A2EB7F80A26DC7FCA2131EA25B137C13785B12 01485A485A485A003FC8FC127E5A12F012601A257F981E>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo rsfs5 5 6 /Fo 6 89 df<171817381770EE01E01607EE0EC01639EE6380923801C300ED0307ED060E 90390FE0181E90393FFC301C9039783F60389039F007C078020313703A01E006E0F09138 0C71E09039C01833C0EC303BED1F801460D9E0C090C7FC3A00E1801E103A3C7B003E30D8 7C3FEB3CE090391FFC7F8027F079FFFEC7FC397FE003F86CC66C5A2D1E7C9D2E>65 D<913903FFC080023F13FB9139F8007F00D90380EB1F80010EC7EA3BC0D91806EB71E001 7014E101C013013A01800E03C192380783C03A03001E0F0392381E0780000690393C3E0F 009138787FFE4A485A260301E113FFD9FFC113C73B01FE03E00780C7EA07C091380F8187 158F91391F3C0F000018EB3E60007C90387CC01E02F85B26F801F05B26C007C05B3AF01F 807FC0277FFC003FC7FCD81FF090C8FC2B1E7D9C33>I<16F80108EB07FC01F8EB1F06D8 07E0133C48C712F0001C903801E00C003CEB03C04890380F801891381F003048013E13E0 91387C038000789038F81E006CEBF1F8001FB512C0000701FCC7FC380007C0A290380F80 C090381F03F8EC0E3C90381E181EEB3E30EB3C60151CECE03CEC607814706DC65A90380F 03C06DB4C7FCEB01FC271F7C9D29>I<EC1FC0ECFFF0010313F890380781DC90380F038C 90381E060CEB3C0C017C131801781330EC0FE0EC0780017BC7FCEB3FE0EA01FF3803CFC0 000FC8FC121E383E03E0387C0FF83878183C38F8301E12F013605C38704078387800F038 3E03E0381FFF80D803FCC7FC1E1D7B9C22>69 D<913807FF80021F13F0027F13FE49B612 F0902603C00113E0903A0701807FC090390C03C0E701189038C1C000013013C3EDC78049 4848C7FC159EEC1F1E90393FFC3C0C9138F07C3E90C7EA787CEDF8F84AB45A023F13C090 3801FFE390260783E6C7FC90380C07C09038000F80001C49C8FC003C133E007C5B00785B 38E001F0EB03C038780F80D83FFEC9FCEA0FF02C207C9D31>I<027F147F902601FFC0EB FF80903B0781F0039F00903A0C0078060ED93810011CC7FC903960383C305ED9C0785BD8 0180EB3D80DAF07FC8FC157E903881E0FCEBC3C03900FF81F890387C1FFF13005DEC07C0 4A5A141F92C9FC5C027E1306003813FE267801E65B26F803C65B26F007865B26C00F035B D8E03CEBC1C0277FF001FFC8FC391FC0007C311F789D36>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi5 5 6 /Fp 6 104 df<146014E0A2EB01C0A2EB0380A2EB0700A3130EA25BA35BA25BA25BA348 5AA2485AA248C7FCA3120EA25AA35AA25AA25AA25A13297B9E1F>61 D<0003B512E015FC15FF3A003E003F80150FED07C05BA3ED0F80491400153E15FC90B512 E05A9038F003F0EC00F8A2485AA44848485AA21630D8FFFC1460913800F8E0ED7FC0C8EA 1F00241D7C9B2B>82 D<903807F02090381FFC6090387FFEE09038F80FC03801E0033803 8001A2D807001380A291C7FC7F7FEA03FC3801FFC06C13F0EB3FF8EB01FCEB003E141E14 0EA21230A200705B143C00785B387E01F0B55A00C71380D881FEC7FC1B1E7B9C24>I<00 0FB612C0A25A3A1E00F80780003814031501383001F012701260A23AC003E00300000091 C7FCA3495AA4495AA449C8FCA3380FFFFCA25C221C7D9B23>I<14F8EB03FCEB073CEB0F 7CA2EB0E38EB1E00A53803FFF05AA238003C00A25BA65BA5485AA4EA71C012FB5B00F3C7 FC12FE123C16257B9C1C>102 D<EB1F18EBFFBC3801E1FC3803C07C38078078EA0F005A A2003E13F0A4EB01E0A2EA1E03EA0F0F3807FFC0EA01F3EA0003A23870078012F8EB0F00 EAF03EEAFFFCEA3FF0161A7C911D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmsy5 5 5 /Fq 5 49 df<127812FCA4127806067A8D13>1 D<13E0A438F0E1E0EAF8E3387EEFC038 1FFF00EA03F8A2EA1FFF387EEFC038F8E3E0EAF0E13800E000A413127B921F>3 D<1318133C137E13FF3801E7803803C3C0380781E0380F00F0001E137848133C48131E48 130E0078131E6C133C6C13786C13F0380781E03803C3C03801E7803800FF00137E133C13 1817177D951F>5 D<EB07F0EB3FFE9038F80F803901C001C048C71260000680000E1438 001B146CD8198013CC3930C0018690386003063960300603EB180C3AC00C180180EB0630 EB0360EB01C0148014C0EB0360EB0630EB0C183A60180C0300EB300639306003069038C0 018639198000CC001BC7126C000E1438000614306C5C3901C001C03900F80F80D93FFEC7 FCEB07F021237B9B2D>10 D<EA0780EA0FC0A4EA1F80A21300A25A123EA2123CA2127C12 78A2127012F0A25A0A157D9612>48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmss12 12 5 /Fr 5 115 df<B612FCEDFFC016F016FC16FF1780902680000F13C0030113E09238007F F0EE1FF8160FEE07FCA2EE03FE1601A217FFA282A45EA217FEA21603EE07FCA2EE0FF816 1FEE7FF0923801FFE0030F13C090B7128017005E16F816E093C7FC0180C9FCB3AB304578 C43E>80 D<B612F8EDFF8016F016FC82707E902680000F7F03017F6F6C7EEE1FF8707E16 07707EA2160183A282A35EA25F1603A24C5A160F4C5AEE7FF0ED01FF030F5B90B75A94C7 FC5E16F816E0168093C8FCEB8000826F7E153F82151F82150F826F7EA26F7E1501828183 707EA2707E161F83707EA2707EA2707EA2707E701380A2EF7FC0324577C43F>82 D<EB01FE903807FFC0011F13F0017F7F90B57E48804880481303260FFC00138049133F48 48EB1FC05B4848EB0FE0A248481307A290C7FCED03F0B7FCA648C9FCA27EA37E7FA2123F 7F7F001F15206D14E0D80FFC13016C6C13073A03FF807FF091B5FC7E6C15E0013F14806D EBFE00010713F8010013C0242F7DAD2B>101 D<12FFB3B3B3AF084579C417>108 D<141F00FE13FF13035B131F5B5BEBFFF0148038FFFE005B5B5B5B5BA25BA390C7FCB3A8 182D79AC21>114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmbx12 12 28 /Fs 28 122 df<ED0FFF4AB512E0021F80027F80903A01FFF803FC01079038C0007E4990 380001FFD91FFC497F49485B137F495AA25C5AA27090C7FC705A705A94C8FCA74BB512C0 B9FCA500019038E00003B3B0B600C1B61280A539467EC53E>12 D<EA07C0EA1FF0EA3FF8 EA7FFCA2EAFFFEA5EA7FFCA2EA3FF8EA1FF0EA07C00F0F788E1F>46 D<ECFFE0010F13FE017F6D7E90B612E0000315F82607F8037F260FE0007FD81F80EB3FFF 48C76C138001E06D13C0486C6D13E07F00FF6E13F07F8117F8A36C5A6C5A6C5A6C5AC8FC 17F05D17E0A24B13C0A24B138017004B5A5E4B5AED7FE04B5A4A5B93C7FCEC03FC4A5AEC 0FE04A5A4A4813F84AC7FC14FC495A4948EB01F0495AEB0F8049C7FC013E140349140790 B7FC4816E05A5A5A5A5A5AB8FC17C0A42D417BC038>50 D<EE1F80A24C7EA24C7EA34C7E A24B7FA34B7FA24B7FA34B7F16BF031F80163F82033F80ED3E0F037E80157C8203FC804B 7E02018115F0820203814B7E0207815D177F020F814B7F021F8292C7FC834A82023E8002 7E82027FB7FCA291B87EA2498302F0C71203830103834A800107835C187F49488284011F 8491C97E4984133E84B6021FB612F0A54C457CC455>65 D<B9FC18F018FE727E19E02600 3FFEC700077F05017F717F727E727EA2721380A2841AC0A74E1380A21A00604E5A614E5A 05035B050F5B94B5128091B700FCC7FC6018FF19E04AC7000113F8716C7E727E95381FFF 80841AC07213E0A27213F0A21AF8A81AF0A2601AE0601AC060067F138095B5120005075B BA12F86119C04EC7FC18E045447CC350>I<DCFFF81430031F01FF14F04AB6EAE0010207 EDF803021FEDFC07027F9039F001FF0F494848C7EA3F9F4901F8EC0FFF010F01E0140349 0180804948C9FC4948167F4948163F485B191F4849160F485B19075A485B190391CAFC5A 1901A25A5B96C7FCA212FFAC127FA36DEF01F07EA37E80F103E06C7F7EF107C06C7F6C6D EE0F80191F6C6D17006D6C163E6D6C5E6D6C6C15FC6D01E0EC03F8010301F84A5A6D01FF EC3FC06D6C9039F001FF80021F90B6C7FC020715FC020115F0DA001F1480030001F8C8FC 44467AC451>I<B9FC18F018FE727E19E0D8003F90C7001F13F805017F716CB4FC061F7F 727F06037F727FA2727F737EA2737EA2737EA21B8085A21BC0A51BE0AD1BC0A51B8061A2 1B00A24F5AA24F5A4F5AA24E5B4E5B4E5B061F5B067F90C7FC4D485A051F13F8BA5A19C0 4EC8FC18F095C9FC4B447CC356>I<B700C0010FB512F8A5D8003F90C9381FE0004F5A4F 5A4FC7FCF001FC4E5A4E5AF01FE04E5A4E5A06FEC8FC4D5A4D5A4D5AEF1FE04D5A4DC9FC 17FE4C5A4C5AEE0FF04C5A4C7E167F4C7E4B7F03077F5D4B7F4B80DB7F3F7FEDFE1F4B6C 7F03F880EDE0074B6C7F4B6C7F03008082717E85717F83717F85717F83717F8583727E72 7F8684727F86727F84B7D8C001B612FCA54E447CC358>75 D<B812F8EFFFC018F818FE72 7ED8001F902680003F13E005077F05017F717F727E727EA28684A286A762A24E90C7FCA2 614E5A18FF4D13F005075B057F138092B7C8FC18F818C018F0DB800013FCEF3FFF717F71 7F83717F8583A285A685A61B1FA2717FA2726C133EA2B700F06DEB807E72EBE0FC72EBFF F8060314F0DE007F13E0CC0007130050457DC354>82 D<003FBA12E0A59026FE000FEBC0 03D87FF09338007FF049173F0180170F190790C7FC007E1803A3007C1801A400FC19F848 1800A5C81700B3B3A20107B87EA545437CC24E>84 D<903801FFF0011F13FF017F14C048 B612F04848C66C7ED807F8EB1FFC486C6D7E6D6D7E486C81818381836C5A6C5A6C5A6C5A C8FCA30203B5FC91B6FC1307013F13F19038FFFE01000313F0481380481300485A485A48 5AA2485AA45DA26C6C5BA26C6C010E13F86C6C013CEBFFC03A0FFF80F87F6CEBFFF06CEC E01FC66CEB8007D90FFCC9FC322F7DAD36>97 D<EB3FE0B5FCA512037EB1ED0FFC92387F FFC002E3B512F002EF14FC9139FFE01FFE92380007FF02FC010113804A15C04A6D13E04A 147F18F018F8A2173F18FCA318FEAB18FCA4EF7FF8A218F0A2EFFFE06E15C06E4913806E 5B023F90380FFE00903AFE1FE03FFCD9FC07B55A496C14E049C61480C8D80FF8C7FC3746 7EC43E>I<EC3FF849B57E010F14E04914F890397FF007FC9039FFC001FE4849487E4849 5A484A1380485AA2485A123F6F13006F5A48486D5A6F5A93C7FCA212FFAA127FA27FA212 3FEE07C06C7EEE0F806C7E6CED1F006C7F6C6D133E6C01F013FC90397FFC03F86DB55A01 0F14C0010391C7FC9038003FF82A2F7CAD32>I<EC3FF849B5FC010F14C0013F14F09039 7FF01FF89039FFC007FC48496C7E48496C7E48481580000F80484815C0167F003F16E0A2 5B127FEE3FF0A212FFA290B7FCA401F8C9FCA5127FA36C7EA2001FED01F0A26C7EEE03E0 6C6C14076C6DEB0FC06C6DEB1F806C01F0EB3F0090397FFE01FE011FB55A010714F00100 14C0DA1FFCC7FC2C2F7DAD33>101 D<913801FF80021F13E0027F13F849B512FC010713 8790390FFE0FFED91FFC13FF49485A137F14F013FF14E048EC0FFEED07FCED03F8ED00E0 1600AAB612F8A5000101E0C7FCB3B0B612E0A528467DC522>I<DAFFE013FC010F9038FE 03FF013FD9FF8F138090B812C048D9C07F1307489039001FF87F4848EB0FFC000F9238FE 3F80491307001F9238FF0E0094C7FC003F82A7001F93C7FCA2000F5D6D130F00075D6C6C 495A6C9038C07FF091B55A481580D8078F49C8FC018013E0000F90CAFCA47FA213F090B6 12C016FC6CEDFF80836C16F0836C826C821203000F82D81FF0C77ED83FC01407007F6F13 80498000FF81A56C6C4A1300A26C6C4A5A6D14076C6C4A5AD80FFEEC3FF83B03FFE003FF E06C90B65A6C6C92C7FC010F14F8D9007F90C8FC32427DAC38>I<EB3FE0B5FCA512037E B1ED03FF031F13E04B13F892B57E9139E1F81FFE9139E3C00FFF9138E78007DAEE008002 FE7F4A815CA25CA35CB3A7B600C1B61280A539457DC43E>I<137C48B4FC487F487FA248 7FA56C5BA26C5B6C90C7FCEA007C90C8FCAAEB3FE0EA7FFFA512037EB3AFB61280A51946 7DC51F>I<EB3FE0B5FCA512037EB3B3B3A3B612C0A51A457DC41F>108 D<90277FC003FFEC07FEB5011F01E090383FFFC04B01F84913F092B56C48B57E913DC1F8 1FFE03F03FFC913DC3C00FFF07801FFE00039026C7800790380F000F6CD9CE00029C8002 DE6D01BC7F02DC03F8158002F85DA24A5DA34A5DB3A7B600C1B60083B6FCA5582D7DAC5D >I<90397FC003FFB5011F13E04B13F892B57E9139C1F81FFE9139C3C00FFF00039038C7 80076CD9CE008002DE7F02DC8114F8A25CA35CB3A7B600C1B61280A5392D7DAC3E>I<EC 1FFC49B512C0010714F0011F14FC90397FF80FFF9026FFC0017F48496C7F4890C76C7E48 486E7E000F8249141F001F82A248486E7EA2007F82A400FF1780AA007F1700A46C6C4A5A A2001F5EA26C6C4A5A00075E6D147F6C6D495A6CD9E0035B27007FF80F90C7FC6DB55A01 0F14F8010114C09026001FFCC8FC312F7DAD38>I<90393FE00FFCB590387FFFC002E3B5 12F002EF14FC9139FFE03FFE9238000FFF000301FC010313806C4915C04A6D13E05C7013 F018F8177FA218FCA2173F18FEAB18FC177FA318F817FF18F0A24C13E06E15C06E491380 6E5B02FF90380FFE009238E07FFC02E7B55A02E314E002E01480DB0FF8C7FC92C9FCADB6 12C0A537407EAC3E>I<90397FC03F80B5EBFFE002C113F802C313FC9138C7C7FEECCF07 00039038CE0FFF6C13DE14FC14F8ED07FEA29138F003FCED00F01600A25CB3A6B612F0A5 282D7EAC2E>114 D<90391FFC038090B5128F000314FF5A380FF003381FC0004848133F 48C7FC151FA248140FA27FA26D90C7FC13F0EBFF806C13FCECFF806C14E015F86C806C80 6C8012016C1580011F14C01301D9000F13E014010078EB007F00F8143FA26C141FA36C15 C0A27E6DEB3F807F6DEBFF009038FC03FE90B55A00F814F0D8F03F5B26E007FEC7FC232F 7CAD2C>I<EB03E0A61307A3130FA3131FA2133F137F13FF5A5A001F90B51280B7FCA400 0101E0C7FCB3A3ED03E0AA6CEC07C014F0017F1480ECF80F90393FFC1F0090381FFFFE6D 5B010313F09038007FC023407EBE2C>I<D93FE0EC7FC0B549B5FCA50003EC00076C81B3 A85EA35E7E5E043B7F6D6C017BEBFF8090393FFC03F36DB512E36D148301031403902600 3FF849C7FC392E7DAC3E>I<B6398007FFFCA5000101F0C7EA7E006C167C8017FC017F5D 6E1301013F5D6E1303011F5D6E13076D5D1580160F6D01C05B161F6D92C7FC6F5A6D143E EDF07E6D147C15F816FC6E6C5A15FD023F5B15FF6E5BA26E5BA36E5BA26E90C8FCA26E5A A26E5AA35D14015D000F1303D83FC05B387FE0075D38FFF00F5D141F92C9FC143E387FE0 7EEBC1FC383F87F8EBFFF06C13C000075BD801FCCAFC36407EAB3B>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft rsfs7 7 6 /Ft 6 89 df<1938197019F0F003E0F00FC0181FF07B80F0E700EF03CFEF071E171EEF38 3C4D5AEE01E093380380F0021F90380701E09138FFF01E903B03F1FC3803C0903B07801F 700780903A0F0007E00FDB01C090C7FC011E496C5A011C0107133E013C90380E703C0138 011C137C03385B017890387039F015E0913901C03BE0913903803FC0133890263C07005B EB1C0ED91E1C1404261E07B8EB3E18263E03F0EB7E30267E00FEEBFCE03BFC01FFF8FF80 28C00383FFFEC8FC90390F0007F0D8F07C6D5AD87FF01307D81F8090CAFC3D2B7DA935> 65 D<923801FFE0030FEBFE1892397E003FF8DA01E0EB03F0DA07801301021EC7EA07F8 0278EC0FBC02E0EC1F1E4948143E902603801C137C902607000C13F8010E90381C01F049 EC03E049913807C03C49EB380F93381F8078499039783F00F09239F03E01E049027E13C0 0001903A01E0FC0380DA03C1B512004A5A91260F03F813800000903A3E07FFE3C09026F9 F80F130190277FE01F8013E0EB0E0090C7EA3F00157E93380F81C09238FC3F03913801F8 F0913A03F1C00780001E9139E3000F00003EEB07C3007ED90F86131E007CD91F065B00F0 D93E0C5B4801FC5CD901F0EB01C03BF003E006078028781F8007FEC7FC3A3FFE0001F0D8 0FF090C9FC372C7CA93C>I<173F933801FF80EE07C1D9078090381F01C0017F143CD801 F0C700F81380D807C0903801E00348C7EA03C0001E91390F80070048EC1F0048023E130E 484A5B4B5B4A485B484948485A0207EB07806C90260FC01FC7FC007090381F807C0078EC 03E0003FD93F3FC8FC000FB512F800031480260001F8C9FCA2495A5C0107EB3FC0494848 7E9138C1C0F0913883807090381F8700140E494813F0133E4A485AA24B5A90393C1C0780 020C90C8FC90383E000E011E5B011F137890380F81E0903803FFC0D900FEC9FC322D7DAA 2E>I<ED07F0ED3FFE92B5FC913903E00780913807800391390F0033C0021E13E191383C 018191397C030380ECF807903A01F00E0700A2903903E00C0E5E9138C00FF8ED07E092C8 FCA2903801FFC0010F7F013F5B9038783F804848C9FC485A485A380F800E391F003FE000 3EEB73F0ECC0784848487EEB0300EAF806A2495B12F05D6CC6485A0078495A6C495A003E 011EC8FC381F807C3807FFF0C613802A2B7DA926>69 D<EEFFF0030713FC031FEBFF8003 7F14E0913A01F8003FFCDA03C090380FFFE0020FC7000113C0021E903980027F80913B38 01C00E0F000270D9E01EC7FCDAE0005B49485C03015BD90380EBE1E0494848485AEEC780 ED078701064948C8FC0107EB1E1E037C497E903B03FFF03E03C06D9038807C0F90C8495A EEF83F053EC7FC923801F7F892383FFFF0913803FFF091391F87E1E091397807C1C09126 E00FC2C8FC903901C01F8090C748C9FC153E000E147E003F5CEC01F0007E495A0078495A 48495A023ECAFC00785B383E03F0381FFFC0D803FECBFC3B2D7DAA3A>I<03FFEC03F802 0301C0EB0FFC91260F03E0133C91263800F0EB70F84A0178EBC0F0913BC0403C03800090 260180E049C7FC0103150ED90700EB3E1C010E5DD91C015C4C5A0138EC7DC0913903C07F 809027300780FFC8FC01705C91380F01FC141E9039387C03F8D91FF05B90390F807FFF90 C7B57E94C8FCED1F804BC9FCA2157E15FE4A5AA24A5A02071407EC0FB0001CD91F30130E 007ED91E705B023C5C4801F8143027F001F0305B27E003C0385B903A07801C038028F81E 001E07C8FCD87FF8EB07FCD80FE0EB01F03E2B77A93F>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmex10 10 2 /Fu 2 96 df<00381707007CEF0F8000FEEF1FC0A26C173F6C1880A26D167F003F1800A2 6D5E001F5FA26D1501000F5FA26D150300075FA26D150700035FA26D150F00015FA26D15 1F00005FA26D153F6D5EA26E147F013F93C7FCA26E5C011F5DA26E1301010F5DA26E1303 01075DA26E130701035DA26E130F01015DA26E131F01005DA26E133F6E5CA2ED807F023F 91C8FCA26F5A021F5BA215E1020F5BA215F302075BA215FF6E5BA36E5BA36E5BA36F5AA3 6FC9FC81150E3A537B7F45>87 D<003C1A1E007E1A3F00FE1B806C1A7FA26D19FF007F1B 00A26D60003F62A26D1803001F62A26D1807000F62A26D180F000762A26D181F000362A2 6D183F000162A26D187F6C62A26E17FF017F96C7FCA26E5E013F60A26E1603011F60A26E 1607010F606E160F010760A26E161F010360A26E163F010160A26E167F6D60A26F15FF02 7F94C8FCA26F5C023F5EA26F1403021F5EA26F1407020F5EA26F140F02075EA26F141F02 035EA26F143F02015EA26F147F6E5EA27013FF037F92C9FCA2705A033F5CA2EEE003031F 5CA2EEF007030F5CA2EEF80F03075CA2EEFC1F03035CA2EEFE3F03015CA2EEFF7F6F5CA2 17FF7090CAFCA3705AA3705AA3705AA216075F1603EE01C051747B7F5C>95 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv bbold10 10 6 /Fv 6 122 df<EB03FE90380FFFC0013F13F090B512FC3901FC03FED807F07FD80FC0EB CF800180EBC7C0D81E00EBC3E0003E14C1003CECC0F05A16785AA31260C7FCA216F0A3ED C1E015C316C0EDC78015CFEDFF005D5D15F0EC0FE04A5A027FC7FCEB01FC495AEB0FE0EB 1F80017FC8FC13FC485AEA03E0485A485A48C9FC121E5A127C1278A25AA2B712F016F8A2 6C15F025387CB72E>50 D<EA7FFC487EA3EAF01EB3B3ADB8128017C0A26C16802A397AB8 33>76 D<007FB512E0B612FE6F7E16E03AF01E001FF0ED01FCED007E82160FEE0780A2EE 03C0A7EE0780A2EE0F00163F167E4B5AED1FF0011FB55A16804BC7FC15E0011EC9FCB3A6 EAFFFEA36C5A2A397AB835>80 D<D87FFC1518486C153CA3EAF01EB3AD00781678A4003C 16F0A3001EED01E0A2001F1503000F16C0019E140700071680D803DEEC0F0001FE5C0001 153E00005D017E5C6DEB03F090391FE01FE06DB55A010391C7FC010013FCEC1FE02E3B7A B83C>85 D<021FEB07C091397FC01FF03B7FFDFFF07FF8B66C487E02E0EBF83E9139803D E01E26F01F0080ED1FC0011EED0780A2ED0F80A2EF03C0A61507B0EAFFFEA216006C486D EB018032267CA53C>109 D<D87FFCEB0180486CEB03C0A26C6CEB0780EA780F3A3C0780 0F00A2391E03C01EA26C6C6C5AA3390780F078A23903C078F0A23901E03DE0A23900F01F C0A29038780F80A2013C90C7FCA2EB1E1EA36D5AA2EB07F8A26D5AA26D5AA2495AA2495A 130F91C8FC131E133E133C5B13F8485A485A485A485A003FC9FC127E5A12F0126022367E A327>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmti7 7 4 /Fw 4 113 df<15F0EC1FF815F0A21401A2EC03E0A4EC07C0A490380F8F80EB7FEFEBF0 FF3803E07F3907C03F00EA0F80497E5A48133E123E127EA2485BA4485B1570A3903801F0 E01303EA7807393C0EF1C0011C1380391FF87F003807E01E1D2979A723>100 D<130E131F133FA2133E131C1300A7EA03C0EA07F0EA0C78121812381230EA70F8A212E0 EAE1F01201EA03E0A3EA07C0A2EA0F801387A2EA1F07130EA2EA1E0C131CEA0E38EA0FF0 EA03C010287BA615>105 D<EB07F0EB3FFCEBF81E48487E3903C00780EA0780000F14C0 EA1F005A003E14E0127E15C048130FA3158048131FA21500143E143C00785B007C5B383C 01E0381F07C06CB4C7FCEA01F81B1B799923>111 D<9038F00FC03901FC3FF039039E78 7839071EE03CEB1FC0000EEB803E1400A2D81C3E133FA21200A249137EA44913FCA215F8 EC01F01201EC03E015C09038FC07803903EE1F00EBE7FCEBE3F001E0C7FC485AA4485AA2 EA7FF812FFA220257E9923>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx xycmbt10 10 22 /Fx 22 127 df<126012F01278127C123C7EA27EA3EA0780A4EA03C0ABEA0780A4EA0300 0A1E879B00>1 D<12C07E7E7E12787EA27EA27EA2EA0780A4EA03C0ABEA0780A3EA0300 0A1E879B00>I<1220127CB47EEA7FE0EA1FF8EA03FCEA007FEB1F806D7EEB03E06D7E6D 7E147880143E141E80A2EC0780A2EC03001915979200>15 D<EB7FF00003B5FC001F14E0 007F14F839FF800FFC00FCC7FC00E014181E079C8400>28 D<EB1FF848B51280000714E0 001F14F8397FE007FC00FEC7127C00F8141800E014001E089C8400>I<EB07FE90383FFF E048B512F8000714FC381FF801393FC0001800FEC8FC12F85A12401E0A9C8300>32 D<903803FF80013F13F848B512FC1207391FFC0078D83FC01300007EC8FC12F85A12401E 0A9C8200>I<903801FFC0011F13F8017F13FC48B5FC3907FE0038D81FE01300EA3F8000 7EC8FC12F85A1E0A9C8200>I<ECFFC0010F13F8013F13FC90B5FC0003EB0038D80FF013 00EA1FC048C8FC127C5A127012201E0C9C8200>I<ECFF80010713F0013F13F890B5FC00 03EB0070D807F81300EA1FC048C8FC127E12F85A5A12401D0D9B8200>I<EC7FF0903807 FFF8131F017F13F03901FF8000D807F8C7FCEA0FE0EA1F80003EC8FC5A5A5A12601D0D9B 8100>I<EC7FE0903803FFF0131F017F13E03901FF8000D803FCC7FCEA0FE0EA1F8048C8 FC127C5A5A5A5A1C0E9A8100>I<143014F81303EB07F0EB1FC0EB3F00137E13F8485A48 5A5B485A120F90C7FC121EA25AA35AA35A127012201519938100>47 D<126012F0A21278A27E123E121E7E7F6C7E6C7EEA01F86C7E137FEB1FE0EB0FFCEB03FF 01001380EC1F0014021915828100>79 D<14201470147814F0A3EB01E0A3EB03C0A2EB07 80130F1400131E133E5B5BEA03F0485AEA1FC0007FC7FC12FE12F812601519829600> 111 D<12075AEA0780A4EA03C0AAEA0780A4EA0F00A2121EA25AA25A12F85A12600A1E82 9B00>120 D<120C121EA27EA4EA0780AAEA0F00A4121EA35A127C12785AA21260091E82 9B00>I<1238123CA2121EA4120FAB121EA4123CA31278A212F0A21260081E829B00>I<12 701278A2123CA2121EA4120FAA121EA4123CA21278A212F0A21260081E829B00>I<12E0 12F0A21278A3123CA3121EAB123CA41278A312F0A21260071E829B00>I<12E012F0A212 78A2123CA2121EA4120FAA121EA4123CA21278A21230081E839B00>I<12E012F0A21278 A2123CA2121EA4120FAB121EA5123CA21218081E849B00>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy xycmat10 10 22 /Fy 22 127 df<EB7FE03807FFFE001FEBFF80007F14E039FF801FF839F80001FC0060EB 007CC8121C1E08828400>1 D<EB3FF80003B5FC001F14E0007F14F839FFC007FC00FCC7 FC0060141C1E07828400>I<1402141FECFF8001031300EB0FFCEB1FE0017FC7FC13FC48 5AEA03E0485A485A90C8FC121E123E123C5AA25AA212601915829200>15 D<13C01201120312071380EA0F00A2121EA25AA25AA45AAB1278A312300A1E839B00>28 D<EA0180EA03C0EA0780120F1300121EA25AA35AA45AAB1278A412300A1E839B00>I<12 07120FA2121EA2123CA21278A412F0AB1278A5123CA21218081E849B00>32 D<1207120FA2121EA2123CA21278A412F0AA1278A4123CA2121EA2120C081E859B00>I< 120E121EA2123CA31278A312F0AB1278A4123CA3121EA2120C071E859B00>I<120E121E A2123CA21278A412F0AA1278A4123CA2121EA2120FA21206081E869B00>I<121C123CA2 1278A412F0AB1278A4123CA3121EA2120FA21206081E869B00>I<1218123CA25AA45AAA 1278A47EA37E121F7EEA0780A2EA0300091E879B00>I<1238123C5AA45AAA1278A47EA2 7EA27EA2EA078013C01203EA01800A1E889B00>I<1220127012F01278A37EA37EA27E7F 12076C7E7F6C7E6C7E137E7FEB1FC0EB07F0EB03F8130014301519939600>47 D<1403EC0780A2EC0F00A2141E143E143C5C14F8495A495AEB0FC0495A017FC7FCEA03FC EA1FF8EA7FE0EAFF80007CC8FC12201915978100>79 D<126012F812FE127FEA1FC0EA07 E06C7EC67E137C7F131E7F14801307EB03C0A2EB01E0A3EB00F0A3147814701420151982 8100>111 D<EA7FE0EAFFFCEBFF806C13E038001FF8EB03FCEB007FEC1F80EC0FC0EC03 E0EC01F01400157015301C0E828100>120 D<EA7FF0B5FC14C06C13F038000FFCEB00FF EC3F80EC0FC0EC03E0EC01F0EC00F8157815301D0D828100>I<EA0FF8EA7FFFB512E014 F8387007FEC77EEC1FC0EC07E0EC03F0EC00F81578153815101D0D828200>I<EA0FFC38 7FFFC0B512F014FC387003FFC7EA3FC0EC0FE0EC03F0EC00F8157C153815101E0C828200 >I<EA0FFE387FFFE0B512F814FE397001FF80C7EA1FE0EC07F0EC01F8EC007C153C1E0A 828200>I<EA07FF007F13F0B512FEECFF80D8780013E0C7EA0FF0EC01F8EC007C153C15 081E0A828200>I<48B47E001F13F0007F13FEB6128039FE007FE00060EB0FF0C7EA01FC EC007C153C15081E0A828300>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmmi7 7 37 /Fz 37 120 df<EB07F0EB3FFCEB7C1F3A01F00F80703A03C007C0E000071303D80F8013 E0D81F00EBE1C05A003EECF180007EEB01F316004814F715FEA25D485C5DA31403007C13 07003C011E13E0003E90387CF8C0391F01F0793A07FFC03F803A01FE001E00241B7D992B >11 D<EC03F0EC1FFCEC3C1EEC700702C013809039018003C01303EB0700010E1307A25B 168049130F1600151E49131C903871FF7801735BA201E113789038E0003C81A24848131F A4485AA448C7123EA2153C157C486C5B5D9038C003E0EC0780261CF03FC7FCEB7FFCEB1F E090C9FC5AA45AA45A22347EA826>I<3907801F80390FE07FE03918F1E0F03938F380F8 3930FF0078EA70FE5B5B00E114F85B1201A23903E001F0A43907C003E0A4390F8007C0A4 391F000F80A2120EC7FCEC1F00A4143EA4143C14381D267D9922>17 D<48B61280000715C0481580481500263C0E07C7FC0070130EEAE01CA21200133CEB381E A21378A213F0A3EA01E0141F1203A2D807C07FA2380F800FA26C486CC7FC221A7D9827> 25 D<ED01C0D80380EB03E00007EC07F048C7FC120E001E1403001C14015AED00E04813 7014F0803AE001F001C0A39138E00380A2ECC0070103140000F06D5A0107131E39F81FF0 3E397FFEFFFC495B6C486C5A6C486C5A390FC00F80241B7E992A>33 D<EB0FF0EB7FFE48B5FC3907E01F80390F000300000E90C7FC5AA4381E7F806C487E5C00 1E90C7FC0038C8FC5AA25AA31408141800705B387C01E0383FFFC0000F5BD803FCC7FC19 1B7E991F>I<1238127C12FE12FFA2127F123B1203A31206A3120C121812381270122008 127A8614>59 D<EC01801403A2EC0700A2140EA35CA25CA35CA35CA2495AA3495AA249C7 FCA3130EA25BA35BA25BA35BA2485AA3485AA248C8FCA3120EA35AA25AA35AA25AA25A19 3B7CAB22>61 D<EB03FCEB0FFF013F13C090387C07E09038F001F09038E000F800011478 486C133C153EA25B6C5AC8123FA3EB1FF8EB7FFCEBF8063901E0033E3907C001FEEA0F80 90C7FC5A4814FC123E127EEC01F85A15F0A214034814E0EC07C0A2EC0F8000781400007C 131E6C137C6C485A6CB45A6C13C0D801FEC7FC202A7CA823>64 D<ED0780150FA2151FA2 153F157FA24B7E15EFEC01CFEC038FA2EC070F140F140E021C7F150714381478147014E0 130114C0D903807FA249B5FC5BA290381C0003A25B5B8249130112015B1203120FD8FFF8 90383FFFC0A25B2A2A7CA932>I<017FB612F017F8A2903903F00007EE00F0A249481470 A4495AED0380A21760494848C7FCA25D5D90383FFFFEA3EC003E017E131CA2EE018017C0 49903838038015189238000700A24848140E161E161C163C48485CED01F8ED0FF0B7FC5E A22D287CA731>69 D<017FB612C017E0A2903903F0000FEE03C0A249481301A4495AED03 81A21780494848C7FCA25D5D90383FFFFEA3EC003E017E131CA4495B151892C8FCA2485A A4485AA3B512C0805C2B287CA72A>I<903B7FFFC03FFFE0A3903B03F00001F800A34948 495AA44948495AA44948495AA449B65AA391C7121F017E4AC7FCA449147EA448485CA448 48495AA3B539807FFFC0A333287CA736>72 D<017FB512C016F882903903F000FFEE3F80 161F4948EB0FC0A44948131FA3EE3F8049481400167E5E4B5A90393F000FE091B5C7FC5D EC001F017E6D7E6F7E82A25BA44848130FA3173048481570A21760B5D8800713E0923803 E1C0923801FF80C9EA7E002C297CA732>82 D<91381FE0189138FFFC380103EBFE789039 07E03FF090380F000F011E13035B49EB01E0137013F0A2000115C0A292C7FC7F7F6CB47E 14F86DB47E6D13F06D7F01077F01007F1407EC00FF153F81A281121CA2003C141EA2151C 153C007C5C007E5C397F8003E09038F00FC000F3B5C7FC00E05B38C01FF0252A7CA829> I<000FB712C017E04816C09039800FC00FD81E0014035A0038EB1F80A2481680A2EC3F00 5AA2481600C7007E90C7FCA45CA4495AA4495AA4495AA4495AA3000FB57E48806C5C2B28 7DA727>I<D87FFFD9FFFEEB7FFCB580495CD80FE0D90FE0EB0FC04CEB0780190000076F 130E181E031F141C033F5CA203775C18F003E75C02014A5A01F013C7DA0387495A0003ED F007DA070391C7FC020F140E140E021C5CA202385C0278147802701470D9F8E05CA22601 F9C0EBF9C0ED01FBD9FB805C01FF02FFC8FC1400495CA2495C5E5B6C485CA2496D5A3E29 7BA73E>87 D<903B1FFFE00FFFC05B6D13C0903B00FE0003F80017E0027FEB078094C7FC 6E130E6F5A021F5B6F5A5E91380FE1C0EDE380DA07F7C8FC15FE6E5A5D6E7EA28114034A 7E4A7EEC1E3F023C7FEC781F02F07FEB01E049486C7EEB078049486C7E131E496D7E5B49 6D7E1207D87FFE90380FFFE000FF4A7F6C485D32287DA736>I<EB0FC0EB3FE09038F873 803801E03F3807C01F1380EA0F0048130F48EB1F00123E127EA248133EA4485B1538A3EC F870EA78011303393C0778E0381E1E7C390FFC3FC03903E00F001D1B7D9924>97 D<EA01E0EA3FF05BA21203A2485AA4485AA4381F1F80EB7FE0EBF0F0EBC078EA3F80EB00 7C123EA248137EA44813FCA438F001F8A214F0EB03E0A2EB07C00070138038780F00EA3C 3EEA1FF8EA07E017297CA71D>I<EB07F0EB3FFCEBFC1E3801F00F3803C01F3807803F12 0F381F003E5A003E1300127EA25AA45AA31404140E0078131E007C133C003C13F8381F03 E03807FF803801FC00181B7D991E>I<1578EC0FFC15F8A21400A2EC01F0A4EC03E0A490 380FC7C0EB3FE7EBF8773801E03F3907C01F801380EA0F0048130F48EB1F00123E127EA2 48133EA4485B1538A3ECF870EA78011303393C0778E0381E1E7C390FFC3FC03903E00F00 1E297DA723>I<EB07E0EB3FF8EBF81C3801E00EEA07C0EA0F80EA1F00A248131C007E13 38EB03F0387FFFC038FFFE0000FCC7FCA45AA214040078130E007C131E003C133C6C13F8 380F03E03807FF803801FC00171B7D991F>I<EC03E0EC0FF0EC1E38EC3C3CEC7C7C15FC 1478ECF8F815701500A2495AA590B512E0A215C0903803E000A3495AA5495AA649C7FCA5 133EA4133C137C123CEA7C78127EEAFCF85BEA78E0EA71C0EA3F806CC8FC1E357CA820> I<EB01F0EB0FFC90381E1EE0EB7C0FEBF807EA01F03803E003A20007EB07C013C0120FA2 391F800F80A49038001F00A35C6C133E147E380780FEEA03C33801FF7CEA007C1300A25C A21238387C01F012FC495A48485A38781F80D83FFEC7FCEA0FF01B267E9920>I<133CEA 07FE5BA2EA007CA25BA4485AA43803E0FCEBE3FF9038EF078001FC13C03807F80313F013 E013C0000F13071380A3391F000F80A3EC1F00123E150E143EA248EB7C1CA21538EC3C30 481470EC1FE00070EB0F801F297CA727>I<130E131F5BA2133E131C90C7FCA7EA03E048 7EEA0C78EA187C1238123012705B12E0A2EA01F0A3485AA2485AA2EBC380EA0F83A2381F 0700A2130EEA0F0C131CEA07F06C5A11287DA617>I<1407EC0F80141FA21500140E91C7 FCA7EB03E0EB07F8EB1E3C1318EB303E137013E0A248485AA2C7FCA25CA4495AA4495AA4 495AA4495AA21238D87C1FC7FC12FC133E485AEA70F8EA7FE0EA1F80193380A61B>I<13 78EA07FCEA0FF8A21200A2EA01F0A4EA03E0A4EA07C0A4EA0F80A4EA1F00A4123EA45A13 38A3EAF870A21360EA78E013C0EA3F80EA0F000E297EA715>108 D<3B07801FC007E03B0FE07FF01FF83B18F0E0F8783C3B38F1807CE03E3B30FF007DC01E D870FEEB3F80491400153ED8E1F8017E133E49137C1201A24848495BA35F4848485A1870 EE01F0A23C0F8003E003E0E0A2EFE1C004011380271F0007C013E3933800FF00000E6D48 137C341B7D993B>I<9038F007E03901FC1FF039031E787C0007EBE03E39061FC01E000E EB801F1400A2D81C3E1480A212001600495BA3153E49137EA2157C5D12014A5A4A5A6D48 5A2603EE0FC7FCEBE7FEEBE1F001E0C8FC485AA4485AA2EA7FF812FFA22125809922> 112 D<90380F8180EB7FE3EBF0F73803E07F3907C03F00EA0F80497E5A48133E123E127E A2485BA4485BA4495A1303EA7807EA3C0F495AEA1FFBEA07E3EA0003495AA4495AA2EBFF F85AA219257D991E>I<3807807E390FE1FF803818F3C33938F703C03830FE073870FC0F A201F8138039E1F0070091C7FC1201A2485AA4485AA4485AA448C8FCA2120E1A1B7D991F >I<EB0FE0EB7FF8EBF03C3801C01E12033807803EA2143C000F1318EBE0006CB4FC14C0 6C13E06C13F06C13F813071301EA3C00007E1378A24813F05A387001E0EB03C0383C0F80 381FFE00EA07F8171B7C991F>I<EA03E0486C1338D80C78137CEA187C00385C12301270 5B00E0495AA2EA01F0A24A5AEA03E0A34848485AEDC380A391380F8700A20003131F9038 E0378E3901F0E7CE3900FFC3FC90383F00F0211B7D9927>117 D<3903E003803907F007 C0D80C7813E038187C0F1238003013070070130313F800E0EB01C0A2EA01F0A2EC0380EA 03E0A2150048485AA21406140E140C141C00035BEBE0303801F0E06CB45A013FC7FC1B1B 7D9921>I<D803E01407486C9038700F80D80C789038F81FC0EA187C0038EB01F0003015 0F0070150713F800E0903903E00380A2EA01F0A2913907C00700EA03E0A33A07C00F800E A2160C161C1618021F1338000315309039E03FC0703A01F073E0E03A00FFE1FF8090261F 807FC7FC2A1B7D9930>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA xydash10 10 35 /FA 35 127 df<1508151C153E157C157815F01401EC03E0EC07C0EC0F80EC1F00141E5C 147C5C495A495A5C495A130F49C7FC133E5B13785B1201485A485A485A48C8FC121E5A12 7C5A5A12601F2482A123>4 D<15101538157815F815F0EC01E01403EC07C0EC0F801500 141E143E5C14785C1301495A495A5C49C7FC5B133E5B13785B1201485A5B485A120F48C8 FC123E123C5A12F85A12601D2582A220>6 D<1580EC01C0EC03E015C0EC0780A2EC0F00 5C141E5C147C14785C13015C495A13075C49C7FC5B131E5B137C13785B12015B485A1207 5B48C8FC5A121E5A127C12785AA212601B2782A41B>10 D<13021307130FA3131EA3133C A41378A313F0A3EA01E0A3EA03C0A3EA0780A4EA0F00A3121EA35AA35AA35AA31260102C 82A90D>21 D<126012F0A21278127C123C7E121F7E6C7E7F12036C7E7F12001378137C13 3C7F131F7F6D7E8013036D7E8013001478147C143C80141F80EC0780A2EC03C015E0EC01 C0EC00801B2782811B>52 D<126012F07E127C123C7E121F6C7E6C7E12036C7E7F6C7E13 7C133C7F131F6D7E6D7E6D7E13016D7E80147C80141E801580EC07C0EC03E01401EC00F0 15F8157C153C15181E24828122>57 D<126012F07E127C123C7E121F6C7E6C7E6C7E6C7E 12001378137C7F7F6D7E13076D7E806D7E6D7E147C143C80141FEC0F80EC07C0EC03E0EC 01F014001578157C153E151C15081F24828123>I<126012F07E127C7E7E6C7E6C7EEA03 F06C7E6C7E133E7F6D7E6D7E6D7E6D7E6D7E147C80806E7E6E7EEC03F06E7E6E7E153E81 ED0F80ED07C015031501222082812A>65 D<126012F07E127C7E6C7E6C7E6C7EEA01F06C 7E137C7F7F6D7E6D7EEB03F06D7E6D7E143E806E7E6E7E6E7E6E7E6E7E157E81ED1F80ED 07C0ED03E0ED01C01500232082812A>I<126012F07E127C123F6C7E6C7EEA03E06C7E6C 7E137C133F6D7E6D7EEB03E06D7E6D7E147C143F6E7E6E7EEC03E06E7E6E7E157C153FED 1F80ED0FC0ED03E015011500231F82812A>I<126012F07E127E7E6C7EEA07C06C7E6C7E EA00FC137E7FEB0F806D7EEB03F06D7E6D7E143E80EC0FC06E7E6E7EEC00F8157C81ED1F 80ED0FC0ED07E0ED01F0ED00E01640241F82812A>I<126012F07E127E7E6C7EEA07C0EA 03F06C7E6C7E133E6D7E6D7E6D7EEB01F06D7E147E806E7EEC07C0EC03F06E7E6E7E153E ED1F80ED0FC0ED07E0ED01F015001660241E82812A>I<126012F012FC127E7EEA0F80EA 07E06C7E6C7EEA007E7F6D7EEB07C0EB03F06D7E6D7E143E6E7E6E7E6E7EEC01F86E7E15 7E151FED0FC0ED07E0ED03F0ED00F81670251D82812A>I<126012F012FC127E7EEA0FC0 6C7E6C7EEA00FC137E7FEB0FC06D7E6D7EEB00FC147E80EC0FC06E7E6E7EEC00FC157E81 ED0FC0ED07E0ED03F0ED00F816781630251D82812A>I<126012F012FC127E6C7EEA0FC0 6C7EEA01F86C7E137FEB1F806D7EEB03F06D7E6D7E143F6E7EEC0FE0EC03F06E7EEC007E 81ED1FC0ED07E0ED03F0ED00F8167C1638261C82812A>I<126012F012FC127E6C7EEA0F C0EA07F0EA01F8EA00FE133FEB1FC0EB07E06D7EEB00FC147E6E7EEC0FC0EC07F0EC01F8 EC00FE153FED1FC0ED07E0ED03F0ED00FC167C163C261B82812A>I<126012F87E127FEA 1F80EA0FE0EA03F0EA01FCEA007E6D7EEB0FC0EB07F0EB01F8EB00FE143FEC1FC0EC07E0 EC03F8EC00FC157FED1F80ED0FE0ED03F8ED01FCED007E161C1608271B82812A>I<1260 12F87E127FEA1F80EA0FE0EA03F86C7EEA007FEB1F80EB0FE0EB03F86D7EEB007FEC1F80 EC0FE0EC03F86E7EEC007FED1F80ED0FE0ED03F8ED01FCED007E161E160C271A82812A> I<126012F87E127FEA1FC06C7EEA03F8EA00FE137FEB1FC0EB07F0EB03FCEB00FEEC3F80 EC0FE06E7EEC01FCEC007FED3F80ED0FE0ED03F8ED01FCED007E161F160E281982812A> I<126012F812FE127FEA1FC0EA07F0EA03FCC67EEB3F80EB0FE0EB07F8EB01FEEB007FEC 1FC0EC07F0EC03FCEC00FEED3F80ED0FE0ED07F8ED01FEED007F161F1607281882812A> I<127012FEEAFFC0EA7FF8EA0FFF000113F038003FFE903807FFC0010013F8EC0FFF0201 13F09138003FFE923807FFC0030013E0EE0FF0EE01E02C1082812A>85 D<1607161F167FED01FEED07F8ED0FE0ED3F80EDFE00EC03FCEC07F0EC1FC0027FC7FCEB 01FEEB07F8EB0FE0EB3F8001FEC8FCEA03FCEA07F0EA1FC0007FC9FC12FE12F812602818 82952A>113 D<160E161F167EED01FCED03F8ED0FE0ED3F80ED7F00EC01FCEC07F04A5A EC3F8002FEC7FCEB03FCEB07F0EB1FC0017FC8FC13FEEA03F8EA0FE0485A007FC9FC12FC 5A1260281982962A>I<160C161E167EED01FCED03F8ED0FE0ED1F80ED7F00EC01FC4A5A EC0FE0EC1F80027FC7FCEB01FC495AEB0FE0EB1F80017FC8FCEA01FC485AEA0FE0EA1F80 007FC9FC12FC5A1260271A82972A>I<1608161C167EED01FCED03F8ED0FE0ED1F80ED7F 0015FCEC03F8EC07E0EC1FC04AC7FC14FEEB01F8EB07F0EB0FC0EB3F80017EC8FC485AEA 03F0EA0FE0EA1F80007FC9FC12FC5A1260271B82982A>I<163C167C16FCED03F0ED07E0 ED1FC0ED3F0015FEEC01F8EC07F0EC0FC0EC3F80027EC7FC5CEB03F0495AEB1FC049C8FC 13FEEA01F8EA07F0EA0FC0EA3F80007EC9FC5A12F01260261B82982A>I<1638167C16F8 ED03F0ED07E0ED1FC0ED3F00157EEC01F84A5AEC0FE0EC1F804AC7FC14FC495A495AEB0F C0495A017FC8FC13FC485AEA07E0485AEA3F80007EC9FC5A12F01260261C82992A>I<16 30167816F8ED03F0ED07E0ED0FC0ED3F00157E5DEC03F04A5A4A5A023FC7FC147E5CEB03 F0495A495A013FC8FC137E5BEA03F0485A485A003FC9FC127E5A12F01260251D829A2A> I<167016F8ED03F0ED07E0ED0FC0ED1F00157E5D4A5AEC07E04A5A4A5A023EC7FC14FC49 5A495AEB07C0EB1F8049C8FC137EEA01F8485A485AEA0F80003FC9FC127E5A12F0126025 1D829A2A>I<166016F01501ED07E0ED0FC0ED1F80ED3E0015FC4A5A4A5AEC07C0EC1F80 4AC7FC147E14F8495AEB07E0495A495A013EC8FC13FC485A485AEA07C0EA1F8048C9FC12 7E12F85A1260241E829B2A>I<164016E0ED01F0ED07E0ED0FC0ED1F80ED3E005D5DEC03 F04A5A4A5A4AC7FC143E14FC495A495AEB07C0495A013FC8FC137E5BEA01F0485A485AEA 1F8048C9FC127E12F85A1260241F829C2A>I<16E015011503ED0FC0ED1F80ED3F00157C 5D4A5A4A5AEC0FC04A5A4AC7FC147C5C495A495AEB0FC0495A49C8FC137C5B485A485AEA 0FC0485A48C9FC127C5A5A1260231F829C2A>I<16C01501ED03E0ED07C0ED1F80ED3F00 157E15F84A5A4A5A4A5A4A5A4AC7FC143E14FC495A495AEB07C0495A49C8FC133E5B5B48 5AEA07E0485A485A003EC9FC5A5A5A12602320829D2A>I<ED01C015031507ED0F80ED1F 00153E15FC4A5A4A5AEC07C04A5A4AC7FC143E5C5C495A495A495A495A49C8FC133E13FC 485A485AEA07C0485A48C9FC123E5A5A5A12602220829D2A>I<ED0180ED03C01507ED0F 80ED1F00153E5D5D4A5A4A5A4A5A4A5A4AC7FC143E14FC495A495AEB07C0495A49C8FC13 3E5B5B485A485A485A485A48C9FC123E5A5A5A12602221829E2A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB rsfs10 10 10 /FB 10 89 df<F30380F307001B0E1B3E63505A1A03F20F70F21EF0F279E0F2E1C0F101 C39638078780F10E0F073C90C7FCF1701EF1E03E953803C03C4EC65A060E13F84E485A03 1F1470912601FFF849485A4A903AFE01C007C0913A0FC1FF8380913C1F001FC7000F8002 3ED907EE49C8FCDC01F85B4A0100143E0278167E02F8496C5B4948D9039C5B9338071E01 4A010E495A0103DA1C0E5B4A9038180F070438495A0107913870071F04E05CDB01C049C9 FCDB03805BDB0700137E010316FEDAE00E5C4B5C6D6C5AD900F8EDF02000036D4890380F E060270F807FE05D271FC01FC090381FC380003FD90FF0D93FC7C9FC007F6DB4149ED980 1E9038FC7FF8277C003C3FB55A00F0D9F00314C0902803E0000FFECAFC26F81F80EB03FC D87FFEC7485AEA3FF8D80FC091CCFC513C7DBA43>65 D<943807FFC0057FEBFC030403B6 1287933A1FE0007FFE047EC7EA07FCDB01F01401DB07C0814BC8487E033CED0FDF037092 381F8F804A48ED3F0FDA0380157E4A48486C13FC020E903903C001F84AED03F04A913880 07E04A150F4A010790391FC01F00F03F804948010F90387F003E4948EC00FEDC1F015C49 C7261E03FC5B043E5B010E4A4848485A050F495A494A4848485A923B01F03FDF8F80DB03 E090B5C7FC4C4813FC923A0780FFC1FFDB0F0101C77F011E013EECFFCF011FD9FC039038 FE07C090270FFFF007EBF8036D9027C00FF0007F903803FE0090C8485A4C5A6293397F80 1C079338FF01FC922701FE07F85B94380F800F922703FC3C0090C7FC922607F8705BD803 80494848133ED80FC0ECE1C0001FDA1FC15C003F4A48485BDB7F03495A48489026FE0700 5B27600001FC4A5A00E0D903F8EC0F80DA07E04AC8FCDA0FC0147CDA3F80EB81F80070D9 7E00EBFFE0267E03F86D1380263FFFE0D900FCC9FC6C018091CAFCD803FCCDFC493E7DBA 4B>I<197EF003FF061F1380F03F0702069238FC03C002FE913803F001D907FCEC07C0D9 1FF091391F800380013EC8EA3F0001F8157C48484A48EB0700D803C04A5A48484A48130E 000F4B5A48C848485B003E4BC75A047E5C484B5C03014A5A484A48495A4B48010FC7FC4B 48131C4B481378033FEB01E0007C91397F800F809226FF007EC8FC003F9138FE03F8261F 8001EB3FC0260FF803B5C9FC0003B612F0C692CAFC010F13F09038001FE04A5AA24A5AED 000F4AEB3FE04948EBFFF0923801E1F8903A03FC0780789139F80E007C5D49485A5DD90F E014785DDAE1C013F802C15C011F14019139C38003E0EC83C04C5A913981E00F80912680 C01FC9FC010FEB001E6E5B16F86D6C485A9138F007C06DB55A010049CAFCEC7FF0423F7E BC37>I<17FF040F13E0043F13F093B512F8923903F800FCDB07E0133E4B48131E92391F 00070E037E131E03FE133E4A4813704B13E0913A03F001C01C0207EB038003E014389139 0FC007001870DA1F8014E0EF01C0DA3F00EB8780EFFF00EE03FCEE00F094C7FC151C9138 1FFFC082ECFFE10103EBFFC0D907E15B90261F807EC8FC49CAFC137E5B485A4848131848 48EBFFC0000F010313F09039C007CFF83A1F800E00FC003F49133C4948133E481330007E 1370146002E0133C48157C495A5E4B5A91380003E0007CC7485A4B5A007E4AC8FC6C143E 6C6C13F8390FF007F06CB512C0000149C9FC38003FF0373C7CBA2F>69 D<4DB47E051F13F0057F13FE4CB67E040715E093261FE00313FC047FC7387FFF8004F802 0F13FEDB01E0020313FCDB0780020013F84BC9121F031E011C90380603F00338013E010E C7FC4B153C4B6D5B4A485D4A48140194383E03E04AC7495A020E4B5A4D48C8FC5CEFF83E 60021849485A0238EB03E0023C90380FC1F0021CD93F03497E021E01FC9038E007C09127 1FFFF007497E6E903AC00FC01DC0912603FC00143991C84848485A07F7C7FC94383F81FE 94387F03F8F0FFE0041FB512804BB6FC92390FFDFC0FDB3F83131F9226F807F890C8FCDA 01E01438913A03800FF0204A484848C9FC91C7FC4C5A4C5A00034BCAFCD80F80495A486C 5C003F4A5A4848495A90C7485A00C04A5A4B5A03FECBFC6C495AEC03F00078EB0FE0007F EB7F80263FFFFECCFC000F13F0000113804F407DBC4A>I<1A100830147F0870EB03FF50 EB0FE04F48EB1F800703EC7E004F4813F8041F4A48485ADC7F80011EEB03C04C6C013E49 5ADB01C34A130FDB03034A49C7FCDB07074948131E030E02035C4B48484848137C03384A 485B93271F003F805B0370D901FF495ADB000FB548485A067E495A932603FCFC49C8FCDC 0001141E4D485B4D485B050F5C9538EE03C094391FFF87804D01CFC9FC94387FC7FC9438 FF87F8F007E04C48B45A4CB55A5E93380FF01F4ECAFC4C485A93383FC07E4C485A178193 38FF01F84B48485A1707DB03FC5BED07F84B48485AD8038014E0D80FC0D91FC01570001F DA3F80495B003F91387F001F03FE4B5A4848494B5A27600001F8010F49C9FC00E0494815 0E4A485DDA1FC0ECC0704AC76C6C5A007001FE6EB45A267E03F86E90CAFC263FFFE0EC00 7C6C018092CBFCD803FCCFFC603E7DBA4C>75 D<943807FFC0057F01FE13100403B6EAC0 38933B1FF0007FF0F0047EC73807FDE0DB01F0913800FFC0DB07C0ED3F8092260F001814 1F033C0138EC3FC00370EE7FE04A48EEFFF0DA0380ED01FB4AC70078EB03F3020E933807 F1F84A0270EB0FE14A02F0EB1FC14AEE3F814A4948148396387F03F04948494813FE4948 1501933A078003FC0749C7270F0387F813E0DC1E0FEBF00F010EDB1F0F14C0933A3C381F E01F49913B78703FC03F8004F002801300922701E0E07F137EDB03C049485A923B0700E1 FE01F8031E4B5A011E499039F3FC07E090261F01F090397FF81F806DB44890263FFFFEC7 FC6D01806D13F8D903FCC714C090C9D83FC0C8FCA24D5A4DC9FC4C5A5F16034C5A4C5AD8 03804A5AD80FC04A5A001F4BCAFC003F15FEED03FC4848495A0070C7EA0FE000F0EC3FC0 4BCBFCEC01FEEC07F80078EB1FE0397E01FF80263FFFFCCCFC6C13E0D803FECDFC4D3E78 BA54>80 D<1B1FF3FF801A03F207C3DD03F8EB1F03053F143E4CB448137CDC0FF8C712F8 047FC7D801F01300DB01F802035BDB07E0EC07E0DB0F80020F130E031EC8EA1FC04B4B48 5A4B5F4BED7F004A484B5B4E485B4A484A48485A505A4E4848C7FC95380FF00E1A3C6F4A 485A020192383FC1E06F4A485ADA00FC039FC8FC037EECFF7C92261FC00113F092260FFE 0313C00303B6C9FCDB007F13F804035B9338001FE04D5AA24D5A4DCAFC4C5AA24C5A4C5A 4C5AA24C5A4C5AD803804A5AD80FC04ACBFC001F4A5A003F4A5A4B5A4848EB0FE00060C7 EA3FC000E04A5A03FECCFCEC03FCEC0FF00070EB3FC0267E01FFCDFC383FFFFC6C13E0D8 03FECEFC513E7DBA48>83 D<DC038013E04C4848481302040E0103140E4C4948133E043C 49C7127C4C49EB01F004F8013EEB03E001FC4A017EEB078048B4494849EB0F0000070203 4948131E290F1F8007C003141CD81C0F010F4A5B011FDA80075C0038D9001F010F5CD870 3E4948485A00E0043F495A4901FFD977C05B2700FC03FE01EF130390B549484848C7FC6D 13FCD93FF1903903BF000E903A0003F8077F0207010E5CEE1CFE91260FF0395CDC71FC5B 91381FE0E3DCE7F85BEDE1C74A484848485ADBC70F495A91287F8E1FE007C8FC159C9338 3FC00EDAFF38495ADB707F5B902601FEE0495A9126FFC0FE5B0380495A49903900FC0780 9127FE01F80EC9FC01075D4A48485AD90FF8EBE0F09139F007E1C002E0495A49484848CA FC0280139ED93F001338ED1E70017EEB1DE0017CEB3F804949CBFC4848137E495B484813 F049485AD807005B000E495A4849CCFC4F3C7BBA43>87 D<DC0FF0ED3FC0DC7FFEEDFFE0 4BB5020313F0922707C03F809038079FE092271E000FC090381E1FC003386D6C01381380 4B6D6C9038700700912601E00C4BC7FC912603801EEC0180DA07006D6C48C8FC020E1606 043E5C4A5E4AD93C035B047C5C4A4B5A4A0178EBF1809326F807F3C9FC902701C001F013 F7EF0FEEDB03E013FCD903805D4B48485A4B48485AED1F00DAC03E495ADAE0F85C6DB448 49CAFC6DEBC00191267E007F13FC91C7B5FC6060DC0FF0CAFC4C5AA24C5A4C5A16FF94CB FC5D4B5A1507A24B48140EED1FDC0003DA3F9C5CD80F80D97F185C486CD9FE385C003FD9 01FC5D277F8003F05D90260007E04A5A00E090260FC03C49C9FC6C90261F801C130E9126 3E001E5B6C01FC011F5B267E03F090380FC0F0263FFFC0903807FFC06C90C76C5BD803F8 DA00FECAFC543C77BA4E>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmti10 10 64 /FC 64 122 df<047FEB03F0923A03FFE007FC030F9038F01FFE923A1F80F83E0FDB3E01 EB7C3F037C1478DBF803EBF87FA20201D901F1133E923AF000E1F01C020302031300A44A 48495AA54A48495AA4010FB812C0A3903C001F80001F8000A34AC7FC4DC7FCA4147E177E A54A5CA54948495AA54948495AA54948495AA44A5C010F140FA24A5CA2011F141F91C790 C8FC001CEB0380003E903807C03E387E1E0F26FE3E1F5B013C1478D8FC78EB81F03A7870 0F03E03A7FF007FFC0263FC00390C9FC390F8000FC404C82BA33>11 D<EE3FFC4BB51280030714C092390FC003E092391F0001F0033C1303037C13075D18E014 014BEB0380020391C7FCA34A5AA54A5AA4010FB612FE835F903A001F80007EA34AC75AA4 4C5AA2147EA24C5AA35C4C5AA44948495AEFC1C0A393381F8380495AA3EF8700A24948EB 0F8F178EEE07FC705A4AEB00F0010F92C7FCA25CA349CAFC121C123EEA7E1EEAFE3E133C 485A1278EA7FF0EA3FC0EA0F80344C82BA2F>I<1307EB0F80131F133FEB7F0013FEEA01 F8485A485A485A48C7FC123E5A12F05A1240111064B92A>19 D<150C153C157815F0EC01 C0EC03801407EC0F00141E5C5C5CA2495A495A13075C130F49C7FC131E133E133C137CA2 5BA2485AA2485AA3485AA2120F5BA2121F90C8FCA35A123EA3127E127CA512FC5AAF1278 A47EA37EA2120E120F7E7F12036C7E12001E5274BD22>40 D<140C140EA2801580140315 C0140115E0A2EC00F0A415F8A21578A4157CA715F8A7140115F0A4140315E0A3140715C0 A2140F1580A3EC1F00A25C143EA25CA25CA25C13015C1303495A5C130F91C7FC131E133E 133C5B5BA2485A485A485A48C8FC121E5A12705A5A1E527EBD22>I<EA01E0EA03F0EA07 F8120FEA1FFCA4EA0FF8EA07B8EA0038A21370A213E0A2EA01C012031380EA0700120E5A 5A5A5A12400E1A7B8919>44 D<387FFFF8A3B512F0A2150579941E>I<120FEA1F80EA3F C0127F12FFA3EA7F801300123C0A0A788919>I<EC03F8EC1FFEEC7FFF9138FC1F809039 01F007C0D903E013E0903807C003EB0F80D91F0013F01501133E017E1303137C13FCA248 5AA2000314075BA2120716E049130F120FA34848EB1FC0A44848EB3F80A448C7EA7F00A3 157E15FE127E5D00FE13015DA248495AA25D007C13075D4A5A141F007E49C7FC003E137E 003F5B381F83F8380FFFE06C1380C648C8FC243A77B72A>48 D<151015381570A215F014 01EC03E0140F141F147F903803FFC0EB1FEFEB3F8FEB1C0F9038001F80A4EC3F00A4147E A45CA4495AA4495AA4495AA4495AA4495AA449C7FCA25B007FB5FCB6128015001D3877B7 2A>I<EC03F8EC0FFEEC3FFF91387C0F809138F007C0903901C003E09039038001F0EB07 00010E14F8131EEB1C30D9387813FC14381370A213E0A33A01C07003F8A214E0ED07F0EB C1C016E09038C7800F9039FF001FC06C4814800178EB3F0090C7127E5D4A5A4A5AEC07C0 4A5A023EC7FC5CEB01F0EB07C0495A011EC8FC5B017014C0491301485A485A48C7EA0380 A2000E1407481500D81FE05BD83FFC131E9038FFC07E39787FFFFCD8700F5BD8F0075BD8 E0015B6D5B48011FC7FC263A79B72A>I<EC03FCEC1FFF4A13809138FC07C0903901E001 E0D903C013F049C712F8130E5B4914FC1460EB70F01470A201E0EB01F8A3D971E013F090 387FC003D93F8013E090381E000790C713C0ED0F80ED1F00153E15FC903801FFF05D495B 9038000FE0EC01F06E7EA281A281A6123C007E495A12FEA248495A5A00E05C4A5AA24A5A 6C495A007049C7FC6C13FE383E03F86CB45A00071380D801FCC8FC263A78B72A>I<ED01 C0ED03E01507A4ED0FC0A3ED1F80A316005DA2153E157E157CA215FC5D14015DA24A5AA2 4A5AA24A5A92C7FC5C141E143E143C5C14F8ECF038903801E07C903803C0FCA2EB0780EB 0F0090381E01F8131C1338137849485AEA01E0EA03C0EA0780390FFC07E0383FFF874813 F726F803FF13803AE0007FFFC048130FC7EBFE0015C04A5AA44AC7FCA4147EA4147C1438 23487CB72A>I<D9607C130CD973FE131C497E01EF143848B5137016F048010713E001F8 13033A07F00387C001C013FF48486C138090C7130048140F001E140E001C141E485CA248 5CA2485C00601301C75B1403A24A5AA24A5AA2141F92C7FC5C143E147EA25CA213015C13 03A25C1307A2495AA3131F5CA2133F5CA2137FA291C8FCA2133E131C263A74B72A>55 D<EC01FCEC0FFF023F138091387E07C09138F803E0903901E001F0903803C000494813F8 49C7FC5B131E133EA3017EEB01F0A2ED03E0A2017FEB07C09138800F8090393FC01F00EC E03E6E5A6D6C5A90380FFFE06D5B6D5B6D7F01077F011F7F90383E1FF89038780FFC4848 6C7E3803E0033807C00148486C7E90C77E5A003E80A25AA248143EA3153C157C15785D14 0100785C007C495A003CEB0F80003E49C7FC381F80FC3807FFF86C13E0C66CC8FC253A78 B72A>I<EC01FCEC0FFE91383FFF8091387E07C0ECF803D901F013E0D903E013F0903807 C001130FEB1F80013F14F8EB7F0015035B5B1201A21507485AA216F0A249130F1207A215 1F16E049133F1203157F16C0000114FF6D5A0000903803BF809038FC077FEB7FFED93FFC 130090380FF0FF90C75AA24A5AA25D14035D4A5A121E003F495A48495A92C7FC00FE133E 485B00705BEB03F0383C0FE0383FFF80D80FFEC8FCEA03F8253A78B72A>I<131E137F5B 481380A314005B6C5A137890C7FCB0120F487E487E127F12FFA36C5A90C7FC123C112478 A319>I<EE01C01603A21607160FA2161F83163FA2167F16FF16EF150116CFED038FA2ED 070FA2150E151E151C1538A203707FA2EDE007A2EC01C014031580EC0700A2140EA25CA2 5C027FB5FCA291B6FC9139E00007F849481303A2495A130791C7FC5B130E5BA25BA25B13 F01201D807F84A7EB56C48B512F0A2020015E0343C7BBB3E>65 D<0103B612FC49EDFF80 6D16C0903B000FF0001FF04BEB0FF81707EF03FC4A5A18FE1701A24A5A1703A34AC713FC 170718F8170F02FE15F0EF1FE0EF3FC0EF7F804948ECFF00EE03FEEE1FF891B612E0495D 17F89139F80003FC707E49486D7EEF7F80A218C04948143FA44948147FA44948ECFF80A2 18005E49C7485A5F4C5A160F01FEEC1FE0EE7FC000014A485AB748C7FC16F816C037397B B83A>I<DB03FE130492391FFF800C92B5EAE01C913A03FE01F03C913A0FF000787CDA1F C0EB1CF8DA7F80130D02FEC7120F49481407494815F0495A49481403495A494815E0137F 49C8FC5B000117C0485AA2485A1880120F5B001F93C7FCA2485AA3485AA45B12FFA41738 90C9FCA25FA25F7E6D4A5AA2003F4B5AA24CC7FC6C6C140E5E6C6C5C00075D6C6C5C6C6C EB03C0D800FEEB0F8090267FC07EC8FC90381FFFFC010713F0010090C9FC363D74BA3B> I<0103B612FC49EDFF8018E0903B000FF0001FF04BEB07F8EF01FC717E4A48147FA2F03F 80A24A48EC1FC0A44AC813E0A414FEA44948153FA4494816C0187FA34948168018FFA219 0049485C60A24D5A495A4D5A60170F49485D4D5A4D5A4DC7FC49C85A4C5AEE03F84C5A01 FEEC1FE0EE7F800001DA03FFC8FCB712FC16E093C9FC3B397BB83F>I<0103B8FC5B7F90 3A000FF000034BEB007F183E181E4A5AA44A5A181CA34AC8FCEE0380A2181802FE49C7FC A35E4948130E161E167E91B512FE495CA2ECF800167C49481338A4494849136018E0A293 386001C049481300EF0380A34948EC0700A2170E171E49C8FC5F177C5F01FE1401160700 01ED7FF0B8FC5FA238397BB838>I<0103B712FE5B7F903A000FF000074B1300187C183C 4A5AA44A5A1838A34AC8FCA21603EF803002FE49C7FCA35E4948130E161EA216FE49B55A A3ECF80049481378A449481370A44948136093C8FCA3495AA449CAFCA413FEA2487EB6FC A25C37397BB836>I<DB03FE130492391FFF800C92B5EAE01C913A03FE01F03C913A0FF0 00787CDA1FC0EB1CF8DA7F80130D02FEC7120F49481407494815F0495A49481403495A49 4815E0137F49C8FC5B000117C0485AA2485A1880120F5B001F93C7FCA2485AA3485AA45B 12FF0303B512C04B14E06F14C092390003F800A290C8FC4C5AA37E6D4A5AA2123FA24C5A 6C7EA26C6C143F6C6C4A5A000315EFD801FCEB01CF6C6CEB078790277FC03F03C7FC9039 1FFFFC01010701F0C8FC01001380363D74BA40>I<0103B512F8A216F090390007F8005D A34A5AA44A5AA44A5AA44AC7FCA414FEA4495AA4495AA4495AA4495AA4495AA4495AA449 C8FCA25B007F13FEB5FC7E25397CB820>73 D<0207B512E017F017E091390003FC005EA3 4B5AA44B5AA44B5AA44B5AA44BC7FCA415FEA44A5AA44A5AA44A5AA44A5A121E123F5A48 495AA248495A4891C8FC00E05B6C13FE00705B387803F8383E0FF0381FFFC06C90C9FCEA 01F82C3B78B82C>I<0103B500E090387FFF80496E90B512C04C6D13809026000FF0C738 1FF8004B15C061061EC7FC4A485C187060EF03C04A4849C8FC170E5F5F4AC712F04C5AEE 03804CC9FC02FE130E163C5E5E903801FC014B7E150F151F903903F839FC1571EDE1FEEC FBC0903807F7809138FE007F5C5C49486D7E5CA2707E495A83160FA249486D7EA3707E49 C7FCA2707EA201FE81A200014B7EB500FC013F13F8A26042397BB840>I<0103B512F849 806D5C9026000FF8C7FC15E0A34A5AA44A5AA44AC8FCA414FEA4495AA4495AA4495AA449 48140C171CA21738495AA21770A2494814F017E01601A249C7EA03C01607A2EE1F8001FE 143FEEFF0000011407B8FC5EA22E397BB834>I<902603FFF8923807FFE0494D13F06D4D 13E0D9000FEFF0004F5AA21977021D4C5AA2DA1CFCEC01CFA202384B485AF0071FA2180E 02704CC7FC181CA2183802E0ED707EA2037E14E0A2D901C04A485AEF0380A2EF0700D903 804B5A170EA2171CD907004A485AA26F1370A2010E4B485AEE01C0A2EE0380494C5AEE07 00A2160E494A495AA2ED1FB8A24902F049C8FC5EA201F05C187E00015DD807F816FEB500 C09039007FFFFC151EDA800E5D4C397AB84A>I<902603FFF091B51280494B14C06F1680 D9000F9139000FF000F007C06F5DA2021D93C7FCEC1CFEA2814A6C140EA26F7EA202705D 6F7EA282DAE00F5CA26F7EA2D901C05D6F7EA349486C6C5BA282150049C7495A167FA301 0E91383F8380A217C3161F4903C7C8FCEE0FE7A349EC07FEA31603495DA2160113F0705A 1201EA07F8B500C014781770173042397BB83E>I<ED03FE92383FFFC092B512F0913903 FC07F891390FE001FC91393F8000FE4AC7127F02FEEC3F80D901F8EC1FC0EB07F04948EC 0FE0131F4A15F04948140749C8FC4916F8485AA2485AA2485AA2120F5B001F160F5B123F A34848ED1FF0A44848ED3FE0A3EF7FC0A2188017FF18005E5F16035F007F4B5A4C5AA24C 5A003F4B5A6D4A5A001F4BC7FC6D495A000F4A5A6C6CEB07F06C6C495A6C6CEB3F802700 FF81FFC8FC90383FFFFC6D13E0010190C9FC353D74BA40>I<0103B612F84915FF6D1680 903B000FF0007FE04BEB0FF0EF07F817034A4814FCA318FE4A5AA44AC7EA07FCA318F802 FE140F18F0EF1FE0A24948EC3FC0EF7F80EFFF00EE03FC4948EB1FF891B612E0178004F8 C7FCD907F0C9FCA4495AA4495AA4495AA449CAFCA413FEA21201B512FCA25C37397BB838 >I<ED03FE92383FFFC092B512F0913903FC07F891390FE001FC91393FC000FE4AC7127F 02FEEC3F804948EC1FC0EB07F84948EC0FE0495A4A15F0495A017F150749C813F8485AA2 485AA2485AA2120F5B001F160FA2485AA34848ED1FF0A44848ED3FE0A3EF7FC0A2188090 C912FF18005E5F16035F6C4B5A9026800F805B91381FC00F4A6C485A003F903970703FC0 9026C0E0305B281FC1C0387FC7FC01E1EB18FE3A0FE38019FCD807F3EB1FF0D803FB5CD8 01FFEB3F806CD9C1FFC8FC90263FFFFC13187F0101013C133890C714301770A292383E01 E0ED3F07EEFFC0A25FA294C7FC5E6F5A6F5AED07E0354B74BA40>I<0103B612E04915FC 17FF9027000FF00013804BEB1FE0170FEF07F04A4814F8A318FC4A5AA44AC7EA0FF8A3EF 1FF002FE15E0A2EF3FC0EF7F804948ECFF004C5AEE07F8EE3FF049B612C04CC7FC5E9138 F8007E49487F8283160F494880A44948131FA44948133FA283A249C7127F1804180EA201 FE161C163F00011738B500FC011F137093380FF0E0933807FFC0C96C13809338007F0037 3B7BB83D>I<92383FC004913901FFF00C0207EBF81C91390FC07E3C91393E001E7C4AEB 07F84A1303495A4A1301494814F013075C130F91C713E05BA34915C0A36E90C7FCA2806D 7E14FCECFF806D13F06D13FE6D6D7E6D806D80023F7F02077FEC007FED0FFC1503150115 00A3167C1206120EA3001E5DA34B5A003E5D15035E003F4A5A48140F6D49C7FC6D133ED8 79F05B39F0FC03F039E07FFFE0011F138026C003FCC8FC2E3D7ABA2F>I<0003B812E05A A2260FF800EB001F01C049EB07C090C71403121E4A5A121C003C178012384A5A12781270 EF07004A5A5AA2481606C7484890C7FCA44A5AA44A5AA44AC9FCA414FEA4495AA4495AA4 495AA4495AA2EB3FF0007FB512F8A3333971B83B>I<267FFFF8903803FFFCB5FC6C5BD8 03FEC8EA7FC06C48ED3F00173CA217385FA25F16015F6D4A5AA200004BC7FC5E160E5EA2 5EA25E5EA26D495A7F4B5A150793C8FC150EA25D153C15385D1480013F5B14815DEC8380 A20287C9FCA2148E149E149C14F8A26D5AA25C5CA25CA291CAFC131EA2363B6FB83E>86 D<B500F8903801FFFE5E4A6D13FCD803FEC8EA7FC00001EE3F00173C5F000016706D5D4C 5A6D14036E495A94C7FC160E013F5C6E133C5E011F14706E5B4B5A010F13036E485A93C8 FC150E01075BECF83C5D01035B6E5AECFDC06DB45AA292C9FC5C6D5A1301A35C1303A35C 1307A35C130FA35C131FA2133F001FB57EA292C9FC37396FB83E>89 D<027FB612F091B7FC18E0499038E0001F92C7EA3FC002FC1580D903F0EC7F004A14FE4A 495A494813034C5A91C75B494A5A010E4A5A4C5A167F494AC7FC5E0118495A90C7485A4B 5A150F4B5A5E4B5A4BC8FC15FE14014A5A5D4A5A4A5A4A5A143F4A5A92C7126002FE14E0 495A4948495A13075C4948130349485C495A017F140749C790C7FC495C485A4848141E48 48143E000F157E484814FE49EB07FC4848133F48B6FCB75AA234397AB833>I<14F8EB07 FE90380FFF1C90383F07BE90387C03FEEBF801EA01F000035CEBE0001207485A4A5AEA1F 80123FA249485A5AA300FE495AA448495AEDC1C0A391381F8380A2143F127C91387F8700 007E13FF393E03CF8E381F0F8F390FFF07FC3907FC03F83901F000F0222677A42A>97 D<133FEA0FFF5A7EEA007EA45BA4485AA4485AA4485A14F8EBE3FEEBEFFF390FDF0F8090 38FC07C001F013E0EBE003EA1FC015F01380A2EA3F00A4007E1307A448EB0FE0A315C048 131FA21580EC3F00A2147E147C14FC007C5B495A383C03E0381E0FC06CB4C7FC6C5AEA01 F01C3B77B926>I<147F903803FFC04913E090381FC1F090383F0078017C13384913F838 01F00100031303EA07E0D80FC013F0EC01E04848C7FCA2123F90C8FC5AA312FEA55AA315 101538007C147015F0007EEB01E0003EEB07C06CEB1F00380F80FE3807FFF86C13E0C690 C7FC1D2677A426>I<ED01F8157F15FF157FED03F0A4ED07E0A4ED0FC0A4ED1F80A4ED3F 0014F8EB07FEEB0FFF90383F07FEEB7C03EBF801EA01F000035CEBE0001207485A4A5AEA 1F80123FA249485A5AA300FE495AA448495AEDC1C0A391381F8380A2143F127C91387F87 00007E13FF393E03CF8E381F0F8F390FFF07FC3907FC03F83901F000F0253B77B92A>I< 147F903803FFC0010F13E090381F81F0EB7E00491378485A485A485AA2485A001F14F090 388001E0003FEB07C0EC3F8048B5120014FC14E090C8FC12FEA65AA2007C14101538007E 147015F0003EEB01E06CEB07C0EC1F00380F80FE3807FFF86C13E0C690C7FC1D2677A426 >I<ED07C0ED0FF0ED1FF8ED3C3CED78FC15F8EC01F915F1EDF0F80203137016005D1407 A44A5AA54A5AA2010FB5128016C016809039001F80004AC7FCA5147EA55CA5495AA5495A A5495AA45C130FA35C131FA391C8FCA2EA1C3E123E127EEAFE3C5B12FCEA78F0EA7FE06C 5AEA0F80264C82BA19>I<EC07C0EC3FF091387FF8E0903901F83DF0903803E01F903807 C00FEB0F80011F14E090383F0007A2137E01FEEB0FC05B1201A249EB1F801203A34848EB 3F00A449137EA45DA20003130114036C6C485A140F3800F83DEB7FF96D485AEB0FC3EB00 03A24A5AA44A5A121C003E495A127E00FE49C7FC147E485B387803F8383FFFE06C1380D8 03FEC8FC24367CA426>I<EB03F013FF5A7EEB07E0A4495AA4495AA449C8FCA4137EEC07 F0EC1FFCEC7FFE9038FCF83F9039FDE01F80EBFF80EC000F485A16C05B49EB1F8012035B A34848EB3F00A3157E485AA35D485A913801F81CA33A3F0003F038A3EDE070127E16E0A2 EDE3C048903801FF80007C6D13000038143C263B7BB92A>I<EB01C0EB03E0EB07F0A214 E014C0EB038090C7FCAB13F0EA03FC487EEA0F1F121CA21238A2485AA3EAE07EA25B1200 A2485AA3485AA3485AA214E0EA0FC0A2381F81C0A3EB0380A2EB0700A2131EEA0FFC6C5A EA01E0143879B619>I<150E151F153F157FA2153E151C1500ABEC1F80EC3FC0ECFFE090 3801E1F014C190380381F8EB0701130EA2131CA2EC03F01338A21300EC07E0A4EC0FC0A4 EC1F80A4EC3F00A4147EA45CA4495AA4495A121C383E07E0127E38FE0FC05C4848C7FCEA 787EEA7FFCEA3FF0EA0FC0204883B619>I<EB03F013FF5A7EEB07E0A4495AA4495AA449 C8FCA4137EED0F80ED3FC0ED7FE09038FC01F0913803C1F0EC0703EC0E073A01F80C0FE0 141891383007C09138700380484848C7FCEBF1C0EBF38001FFC8FC485A6D7E14E014F838 0FC3FCEBC0FE143FA248486C7EED81C0A33A3F003F0380A3ED0700127EA2EC1F0E5D48EB 0FFC007C6D5A0038EB01E0243B7BB926>I<EB0FC0EA03FF5A7E38001F80A4EB3F00A413 7EA45BA4485AA4485AA4485AA4485AA4485AA448C7FCA4127E130EA3485AA45BA2EA7C70 A2EA3FE06C5A6C5A123B79B915>I<D801E001FEEB07F03C07F803FF801FFC260FFC0F90 38C07FFE3C1E3E1F07E0F83F001C903B3C03F1E01F8026383F70EBF380913AE001F7000F 02C013FE007018C002805B4A4848EB1F80485A017E5CA21200494948EB3F00A3187E4848 495AA3604848495A943801F81CA34848903A3F0003F038A3F0E0704848137E19E0A2F0E1 C0484849903801FF80000F027C6D13006CC70038143C3E2679A444>I<D801E013FE3A07 F803FF80260FFC0F7F3A1E3E1F07E0001C90383C03F038383F70ECE00114C00070811480 4A485A485A137EA2120049495AA34B5A485AA34B5A485A92383F0380A3484890387E0700 A3ED7C0E485A5EA25E4848EB3FF0000F6E5A6CC7EA0780292679A42F>I<147F903803FF C04913E090381FC1F090383E00F849137C49137E4848133E12034848133F485AA2485AA2 003F147F90C7FC5AA300FE14FEA315FC14014814F8A2EC03F0A2EC07E0007CEB0FC01580 007EEB1F00003E133E6C5B380F83F83807FFE06C5BC648C7FC202677A42A>I<90390780 07C090390FE01FF090391FF07FF8903938F8F87C9138F9E03E903970FF803F4B7E495A17 805CA23801C1F8A3EA00014948133FA44948EB7F00A3167E494813FEA25E4B5AEB1F804B 5A5EECC007013F5C4B5A6E48C7FCECF07E90387E7FF86E5AEC0F8091C9FC5BA4485AA448 5AA3387FFFC0B5FC6C5B293580A42A>I<ECF803903807FE0790380FFF0F90383F079E90 387C03BE9038F801FEEA01F0000314FCEBE0001207485AEC01F8EA1F80123FA290380003 F05AA300FEEB07E0A448EB0FC0A4EC1F80A2143F127CEC7F00007E5BEA3E03381F0FBF38 0FFF7EEA07FCEA01F0C7FC5CA4495AA4495AA2130748B512C0A21580203577A426>I<39 03C003F03907F00FFC390FF83FFE391C7C7C1FECF00F3A387FC01F80153F00709038807F 001400153E017E131C484890C7FCA31200485AA4485AA4485AA4485AA4485AA448C9FC7E 120E212679A423>I<14FE903807FF804913C090381F03E090383C00F049137001F813F0 EBF00100011303A215E00003EB01C06DC7FC7F3801FFC014F8806C7F6D7E6D1380130F01 0013C0141F140FA2123C127E00FE1480A2481400485B00E0131E00705B0078137C383E03 F06CB45A6C5BD801FEC7FC1C267AA422>I<1307EB0F80131FA4EB3F00A4137EA45BA2B5 12FC14FE14FC3801F800A3485AA4485AA4485AA4485AA448C7FC1438A21470127E14E0A2 EB01C0A2EB0380383E0700131EEA1FFC6C5AEA03E0173578B31C>I<13F8D801FEEB01C0 486CEB03E039070F8007120E121C1238ED0FC0EA301F1270A23AE03F001F80A3EA007EED 3F005BA34848137EA448485B160EA3913801F81CA31638140300011307020E13702600F8 3C13F090397FF87FE090393FF03FC090390FC00F00272679A42D>I<01F0130ED803FC13 1F486C5BD80F1FEB7F80121C153F0038141FA24848130FA21600D8E07E7FA3C6485B150E 485AA348485BA35D485AA25DA2156015E05D14014A5A000349C7FC6D5A3801F81E3800FF FCEB3FF0EB0FC0212679A426>I<01F01507D803FC903903800F80486C903807C01FD80E 1F010FEB3FC0121C171F0038160FED1F8048481507A21880D8E07E90383F0003A3C64815 07037E1400485AA3484849130EA4484848485BA35FA25FA202035C1203D9F007495A0001 90390EFC03803A00FC1E7E0F90277FFC3FFFC7FC90393FF00FFC90390FE003F0322679A4 37>I<903907E007C090391FF01FF090393FF83FF89039783C783C9038E03EE02601C01F 137ED80380EBC0FED80700EBC1FC1581000EEC80F816704849C7FCA3C7FC147EA45CA449 5A1670A3261C03F013E0123E007FEC01C0130700FEEC0380D8FC0FEB070039780EF80E90 383C783C393FF83FF86C486C5A3907C00FC027267CA427>I<13F0D803FCEB01C0486CEB 03E0D80F1F1307121CA21238ED0FC0485AA3D8E07EEB1F80A3C65AED3F00485AA3484813 7EA448485BA44A5AA314035D00031307EBF00F3801F83F6CB55AEB7FF7EB1FC7EB00074A 5AA25D001E131F003F91C7FC485B147E007E137C007C5B387001F0387803E0383C0FC0D8 1FFFC8FC6C5AEA03F0233679A428>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FD msam10 10 1 /FD 1 14 df<0060131800F0133CB3A8023FB6FC1880A21800023CC9FCB3A80060131831 3A7BB93C>13 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FE cmr7 7 12 /FE 12 94 df<B512FEA317037CA121>22 D<1306130C13181330136013E0EA01C0EA03 80A2EA07005AA2121EA35AA3127C1278A412F8AD1278A4127C123CA37EA37EA27EEA0380 A2EA01C0EA00E0136013301318130C13060F3B7AAB1A>40 D<12C012607E7E7E120E7EEA 0380A2EA01C013E0A2EA00F0A31378A3137C133CA4133EAD133CA4137C1378A313F0A3EA 01E0A213C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3A2B812E0A3C7 000EC8FCB3A22B2B7DA333>43 D<EB3F803801FFF03803E0F83807803C48487E001E7F00 3E1480A2003C1307007C14C0A400FC14E0AE007C14C0A36CEB0F80A36CEB1F006C131E6C 6C5A3803E0F86CB45A38003F801B277EA521>48 D<13381378EA01F8121F12FF12FE12E0 1200B3AAB512F8A315267BA521>I<13FF000313E0000F7F381E07F8383801FC486C7E00 78137F00FC7F6C1480A2141FA2127CC7123F1500A2147EA25C5C495A495AEB078049C7FC 131E5B13709038E00380EA01C0EA03803907000700120E1218003FB5FC5AB55AA319267D A521>I<13FF000713E0487F381F01F8383C00FC147E007E137F80A3003C5BC7127EA25C 5C495AEB0FE03801FF8091C7FC380003E0EB00F8147C147E80A21580A21238127C12FEA2 1500485B0078137E5C383F03F86CB45A000713C0C690C7FC19277DA521>I<1438147814 F8A2130113031307A2130E131C1338A2137013E0A2EA01C0EA0380EA0700A2120E5A1218 12385A5AB612E0A3C7EAF800A890383FFFE0A31B277EA621>I<B812E0A27ECBFCAB007F B712E0B8FCA22B117D9633>61 D<EAFFC0A3EAE000B3B3B1EAFFC0A30A3B7AAB13>91 D<EAFFC0A31201B3B3B112FFA30A3B7FAB13>93 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FF cmmi10 10 54 /FF 54 123 df<EC3FC0ECFFF0010713FC90380FE07E90263F801F131C90397E000F8049 14C0484801071338484814E0485A03031370484814F0001F16F04915E0123F90C7EBF1C0 5AEEF380A200FEEDF70016FEA25E5E485DA382127E150F151F003E027D13186C02F11338 390F8007E03B07E03FC07C706CB538007FE06C01F8EB3FC026003FC0EB0F802E267DA435 >11 D<ED03F8ED0FFF033F138092387C07C09238F001E0DA01C013F09139038000F84AC7 FC140E4A14FC5CA25C17F85C1601494814F0A24948EB03E0A2EE07C049C7EA0F80EE1F00 913801FF7E02075BD90E0F13F06E7F913803FE7C91C77E49141E161FA2EE0F805BA317C0 5BA3178049141FA40001ED3F005B167E7F00035D5E4B5A6D495AD80770495A0178495A6D 013FC7FC90381F01FE390E0FFFF8010313E0010090C8FC91C9FC5AA45AA45AA45A12602E 4B7FBA2F>I<EC0F80EC3FF891B512804914C014C0903803807F0107EB1F809138000F00 92C7FC80A36D7EA2806D7EA2806D7EA2147E147F808149B47E01077FEB0FEF90383F0FF0 EB7C0701F87F3801F003EA03E01207496C7EEA0F80121F1300481300A2127EA3485C1401 A35DA214035DA2007C495A5D140F6C91C7FC001E131E6C5BEBC0F83803FFF06C5BD8003F C8FC223D7DBB25>14 D<D803E0137F3A07F803FFC0486C4813F03A1C3E1F81F8EC3C0026 383F7813FC5C007049137C5C5C91C712FC485A137EA2120049EB01F8A44848EB03F0A448 48EB07E0A44848EB0FC0A44848EB1F80A44848EB3F00120F6CC7FCC8FC157EA45DA44A5A A44A5AA25D6E5A26377EA429>17 D<14035CA5EDFFC04A13E0143F91B5FC903903FC7F80 D907F0C7FC495A495A495A91C8FC5B13FEA3485AA512007FA2137F90383FBFF06DB47E6D 7F495B90383F7FE0017CC8FC13F0485A485A485A120F90C9FC5A123EA2123C127CA312FC A3127E127F7FEA3FE0EA1FFC13FF6C13E0000313F86C13FF6C6C13C0010F7F01037F9038 007FF8140F14031400A4011E5B90381F81E06DB45A01035BD9007EC7FC234B7EB924>24 D<013FB612E090B712F05A5A4816E0270F80700EC7FCEA1E00001C13E048141E48141C13 0100E013C012000103133CA214801307A2157CEB0F00A25BA2131E133EA25BA201FC137E A25B0001147FA248487FA249131E6C48130C2C257EA32F>I<027FB512C00103B612E05B 131F4915C090267F81FEC7FC9038FC007E48487FEA03E048487F000F81485AA248C7FCA2 127EA3484AC7FCA3153E157E5A5D5D14015D6C495A007C495A5D6C011FC8FC6C133E380F 81FC3807FFF06C5BC66CC9FC2B257DA32F>27 D<013FB512FE90B7FC5A4815FE4815FC26 0F801CC7FCEA1E00001C133C5A48133814785AC7FCA25CA31301A25CA21303A3495AA313 0FA25CA2131FA349C8FC7F130E28257EA324>I<EC3FE0903801FFFC010713FF011F1480 90397F801FC09038FC0007D801E0EB0180484890C7FC5B48C9FCA57F3803C0F03801EFFE 6CB5FCA200035BD80780C8FC48C9FC121CA25A5AA35AA26C14180070141C5D00785C003E 495A391F800FC06CB55A6C91C7FC000113FC38003FE022287FA527>34 D<EE1F800160EC7FE001E0903801FFF048484913F848484913FC48C7EA0FC092381F003E 000E023C131E0338130E484A130F15F05D48495AA24A48130E5A4AC7FCA21406020E141C 12F0020C14380070131C177017F0007849EB01E0EE03C06CED0780003E0178130F6CED3F 00260FC07013FED807F8EB03F83A03FFF01FF06C90B55A6C1580013F49C7FC010F13F801 0113C0D903E0C8FCA25C1307A4130F5CA2131FA349C9FCA2133E131C30377DA436>39 D<126012F87EB4FC13C013F0EAF3F8EAF0FEEB3F806D7EEB07F0EB01FC6DB4FCEC3F80EC 0FE0EC03F8EC01FEEC007FED1FC0ED07E0A2ED1FC0ED7F00EC01FEEC03F8EC0FE0EC3F80 02FFC7FCEB01FCEB07F0EB1FC0495A01FEC8FCEAF3F8B45A13C090C9FC12FC5A12602328 7DA82A>46 D<121E123FEA7F80EAFFC0A4EA7F80EA3F00121E0A0A7A8917>58 D<121E123FEA7F80EAFFC0A213E0A2127F123F121E1200A4EA01C0A3EA0380A2EA0700A2 120E5A123C123812100B1A7A8917>I<150C151EA2153CA31578A315F0A3EC01E0A3EC03 C0A3EC0780A3EC0F00A3141EA35CA35CA35CA3495AA3495AA2495AA349C7FCA3131EA35B A35BA35BA3485AA3485AA3485AA348C8FCA3121EA35AA35AA35AA212601F537BBD2A>61 D<177017F01601A21603831607A2160F161FA2163FA2167716F716E7ED01C783ED0387A2 ED0703150F150E151CA215381578157015E083EC01C0A2913803800114071500140EA25C A2023FB5FC5CA29139E00001FFA249487F13035C49C8FCA2130EA25B133C133801781680 EA01F8D807FC5C267FFFC0017F13FEB516FF18FE383C7DBB3E>65 D<0103B77E4916F06D16FC903B0007FC0003FE4BEB00FFF07F80F03FC04A5A19E0A2181F 4A5A183FA34A4815C0187F198018FF4A4815004D5A4D5A4D5A4AC7EA1FF0EF7FC04C485A 92B500FCC7FC5B17FF4AC7EA7FC0EF1FE049486E7E84170784495A1703A349481407A449 484A5AA260171F49484A5A4D5A604C48C7FC4948495A4C5A01FFEC3FF0007F90B65AB8C8 FC16F83B397DB83F>I<0103B7FC18E018F8903B0007FC0007FE4BEB01FF9438007F80F0 3FC04A48141FF00FE019F018074A5AF003F8A34A4815FCA44A5AA44AC81207A4494816F8 180FA3494816F0181FA219E04948153F19C0A2F07F80495AF0FF0060170149484A5A604D 5A4D5A49484A5A4D5A4DC7FCEE01FE4948495AEE0FF001FFECFFC0007F90B6C8FCB712FC 16C03E397DB845>68 D<0103B812F05B7F90260007FCC7123F4B1407F003E018014A5AA4 4A5A19C0A34A5A1770A219804A4849C7FCA31601DAFF005B1603161F92B5FC495DA29138 FE001F160F49486DC8FCA44948010E130360A2040C130E494890C7FC60A2183C49481538 1878187018F0495A4D5A17034D5A4948141F177F01FF913803FF80007F90B7FCB9C7FCA2 3C397DB83D>I<0103B812E0A390260007FCC7127F4B140FF007C018034A5AA44A5A1980 A34A5AA217C005E013004A484848C7FCA31603DAFF005B1607A2163F4990B5C8FCA39138 FE003F4948131EA44948131CA44948131893C9FCA3495AA4495AA4495AA2497E007FEBFF C0B67E5D3B397DB835>I<0103B5D8FC07B512F8495D6D8190260007FCC7380FF8004B5D A34A484A5AA44A484A5AA44A484A5AA44A484AC7FCA44AC7485AA392B6FC495EA24AC712 03A249484A5AA449484A5AA449484A5AA449484A5AA449484A5AA449484AC8FCA201FF5C 007F01FF90B512FEB600818003015C45397DB845>72 D<0103B512FC4914FE6D14FC9039 0007FC005DA34A5AA44A5AA44A5AA44A5AA44AC7FCA4495AA4495AA4495AA4495AA4495A A4495AA4495AA213FFB67EA292C7FC27397DB824>I<0103B500FC90380FFFFC495E6D70 13F890260007FCC7000113804BEDFC0019F04E5A4A48EC07804EC7FC181C604A4814F04D 5AEF03804DC8FC4A48131E5F17705F91397F8003C04CC9FC160E161E9138FF007E16FF5D 15074948487FED1C7F03387FEDF03F903803FDE0DAFF807FED001F4A804948130F5C8316 074948801603A283494813018382A249486E7EA284173F494881A201FF4B7E007F01FF01 0FB57EB61280150046397DB847>75 D<0103B6FC5B7F90260007FEC8FC15F8A34A5AA44A 5AA44A5AA44A5AA44AC9FCA4495AA4495AA4494815C01701A2EF0380495AA2EF0700A249 485C170E171EA249485C177C17FC4C5A49481307EE1FF001FF14FF007F90B6FCB85AA232 397DB839>I<0103B7FC4916E06D16F8903B0007FC0007FC4BEB01FEEF007F19804A48EC 3FC0A319E04A5AA44A48EC7FC0A319804A4814FF19004D5AA24AC7485A4D5AEF0FE0EF3F C0494849B4C7FC91B612FC17F094C8FCD903FCCAFCA4495AA4495AA4495AA4495AA4495A A213FF007F13FFB67E92CAFC3B397DB835>80 D<4BB4FC031F13F092B512FC913903FE01 FE913A07F0007F80DA1FC0EB3FC04A48EB1FE002FEC7EA0FF0494814074948EC03F8495A 494815FC49481401013F16FE495A49C8FCEF00FF485A12035B12075B120F495D121FA248 5AA34848ED03FEA44848ED07FCA3EF0FF8A218F0171F18E090C9123F18C06DED7F80127F EFFF00913903E001FEDA0FF05B003F496C485A9039C03C3C07001F9039700C0FF0903AE0 E00E1FE0000FED3F802607F1C049C7FC01F9EB06FED803FDEB07F8D801FF495A3A007FE0 7FC06DB5EA000313070100018F5BDA000F1306170EEE801E5FEEC0FCEEFFF8A25F5F5F81 94C7FC6F5AED00F8384B7CBA42>I<0103B612F849EDFF806D16E0903B0007FC001FF84B EB03FC717E717E4A48801980A219C04A5AA44A48ECFF80A34D13004A485C1703604D5A4A C7485AEF3FC0EFFF80DC07FEC7FC4990B512F817C0A29139FE001FE04948EB07F0707E70 7E8349481300A449481301A449481303A44948495A194019E0A24948ED01C0160301FFEE 0380007F01FF903901FE0700B6D88000130E92C7EA7FFCCA6C5AEF07F03B3B7DB83F>I< 92381FE0019238FFFC030203EBFE0791390FE01F0F91391F80079F91393E0001FE5C4A13 00495A4948147C13075C130F4A1478131FA3013F1570A28017008080EB1FFCECFF8015F8 6DEBFF806D14E0826D800100806E7F020F7F1400031F1380150181167F163FA30006151F 120EA3001EED3F00A2163E167E003E157CA25E003F4A5A484A5A6D495AD87DE0495AD878 F0013FC7FCD8F07F13FE39E03FFFF8010F13E0D8C00190C8FC303D7CBA33>I<48B812FE 5A5A903AFC003FE00301E09138C0007ED80F80163C90C7FC000E4A5A121E121CA2484AC7 FC18385AA24A5A5AA2481730C748481400A44A5AA44A5AA44A5AA44A5AA44A5AA44AC9FC A4495AA4495AA2EB0FFE003FB67EA337397EB831>I<003FB5D8C003B51280485D6C8126 007FC0C7383FF0004AEC0F8095C7FCA249C8120EA448485DA448485DA448485DA448485D A448484A5AA448484A5AA448484AC8FCA448C8120EA35EA25EA25E6C5DA24B5A6C4A5A6C 6C49C9FC151E6C6C5B6C6C13F83903F807E0C6B512806D48CAFCEB0FF0393B7BB839>I< 267FFFFE91387FFFC0B5FC7E0001018091380FFC0091C8EA07E0715A4D5A6C94C7FC5F17 0E5FA25F17786E14705F017F14015F4C5AA24CC8FC5E6E130E5EA2013F5C167816705EA2 4B5A6E485AA24BC9FC011F5B150E5DA25D1578ECF0705D130FECF1C0ECF380A202F7CAFC 14FF5C5CA26D5AA25C5CA25CA25C3A3B7CB830>I<277FFFFC01B500F090B51280B56C48 6E5A6C496C4A7E0003902780000FFCC7381FF8006C48C749EC07E01B80A2040793C7FC1A 0EA262A2040F5D1A78041F157062163F6D027F4A5A16776C03E74A5A83DB01C74AC8FC61 DB0383140E03075D1603030E5DA2031C5D19F003385D4E5A1570DA80F04A5A15E090267F 81C04AC9FC715ADA8380140E0401131EDA8700141C028F5D148E029C5DA202B85D17FF02 F05D605C95CAFC5C6D485CA291C75B705A133E5F133C01385D513B7CB84E>I<91B500FC 90B512E0495D83D9000301C090381FFC006E90C7EA0FE0198096C7FC6E6D131E60606F6C 5B4D5A6F6C485A604DC8FC92381FF00E5F030F133C705A5F923807FDE0EEFFC05F6F90C9 FC5E6F7EA36F7F5D5D4B7F167F92380E3FE0151C15389238781FF015F0913801E00FDA03 C07FEC07804A486C7E140E5C4A6D7E5C02F06D7E495A495A49486D7F49C8FC49157F017F 4B7E2603FF8001037F007F01F0011FEBFF80B56C5B6C497F43397EB845>I<147E903803 FF80010FEBC38090391F81E7C090383E00FF49137F5B4848EB3F80485A12074848131FED 3F00485AA2123F90C7127E5AA300FE5CA44A5A48151CA3913803F038A2007C1307140F00 7E011F1370003E133B6C01F113E0380F83E13A07FFC0FFC06C9038807F803A00FC001F00 26267DA42C>97 D<133FEA0FFF5AA2EA007EA45BA4485AA4485AA4485A14FCEBE3FF01E7 13C0390FDF07E09038FC01F013F801F013F8381FE0004913FC5BA248C7FCA4007E1301A4 48EB03F8A315F014074814E0A2EC0FC0A2EC1F801500007C133E147E003C5B383E01F038 1F07E06CB45A6C90C7FCEA01FC1E3B7CB924>I<EC3FC0903801FFF0010713FC90380FE0 3E90383F800E90387E001F49133F4848137F484813FF485A15FE4848137C001F14384913 00123F90C8FC5AA312FEA55AA31502007C1407007E140E151C003E14386C14F0390F8003 E09038E03FC00003B512006C13FC38003FC020267DA424>I<163FED0FFF5DA2ED007EA4 16FCA4ED01F8A4ED03F0A4ED07E0147E903803FF87010F13C790391F81EFC090383E00FF 49137F5B4848EB3F80485A12074848131FED3F00485AA2123F90C7127E5AA300FE5CA44A 5A48151CA3913803F038A2007C1307140F007E011F1370003E133B6C01F113E0380F83E1 3A07FFC0FFC06C9038807F803A00FC001F00283B7DB92B>I<EC3F80903801FFF0010713 F890381FE07C90383F003C017C131E5B485A1203485A485A001F143C491378003FEB01F0 EC07E048B512C0150014F890C8FC127E12FEA6127E15021507150E003E141C003F14386C 14F0390F8003E03907E03FC06CB512006C13FC38003FC020267DA427>I<16F8ED03FE4B 7E92380F0F80ED1E1FED3E3FED7C7FA203FC1300163E161C4A48C7FCA54A5AA54A5AA201 03B512F05B5E9026000FC0C7FCA54A5AA64AC8FCA5147EA55CA5495AA5495AA45C1307A2 5C121E003F5BEA7F8FA2D8FF0FC9FC131E127EEA7C3CEA3FF86C5AEA07C0294C7CBA29> I<EC07E0EC1FF891387FFC389138FC1E7C903903F007FCEB07E090380FC003D91F8013F8 1400491301137EED03F05B1201A249EB07E01203A34848EB0FC0A4ED1F805BA3ED3F0000 035CA26D5B0001495A3800F80790387C1F7EEB3FFE90381FF8FCEB07E090C7FCA24A5AA4 001E495A123F486C485AA24848485A4A5A007E017FC7FC387C01FE383FFFF86C13E00003 90C8FC26367FA428>I<EB03F013FF5AA2380007E0A4495AA4495AA449C9FCA4137EEC03 F8EC1FFE4A6C7E9039FCFC0FC09038FDE007D9FFC07F148048EB00035B5B49130712035B A34848495AA34B5A485AA24BC7FCA2485A92387E0380A348C738FC0700A3EDF80E127E5E 5EED787848EC7FF0007C6E5A0038EC0F80293B7CB930>I<14E0EB01F0EB03F81307A214 F0EB03E0EB01C090C7FCAB13F8EA01FEEA07FF130F000E1380121C1238A2EA701FA338E0 3F00A3EA007EA25BA3485AA3485AA23807E038A3380FC070A3EB80E0A2EB81C0EB838038 07870013FFEA03FCC65A15397EB71D>I<150E151FED3F80157FA21600153E151C92C7FC ABEC0F80EC3FE04A7EECF0F8EB01C049487EEB0700A2130E5BA24A5A1338A213004A5AA4 4A5AA44A5AA44A5AA44AC7FCA4147EA45CA4381E01F8123F387F83F05CEAFF07495A4848 5AD87C3FC8FCEA3FFC6C5AEA0FC0214981B722>I<EB03F013FF5AA2380007E0A4495AA4 495AA449C8FCA4137EED07C0ED1FE0ED3FF049EBF838913801E0F8EC0381EC07033901F8 0E07141C143891387003F03A03F0E001C0D9F1C0C7FCEBF38001FFC8FC485A6D7E14F014 FC380FC1FEEBC07FEC1F80A248486C7E1670A33A3F001F80E0A3ED81C0127E020F138015 8391380787004814FE007C6D5A0038EB00F8253B7CB92B>I<EB0FC0EA03FF5A7E38001F 80A4EB3F00A4137EA45BA4485AA4485AA4485AA4485AA4485AA448C7FCA4127E1307A3EA FC0EA35BA3EA7C381378EA3FF06C5AEA0780123B7DB919>I<D803E0017F14FE3D07F803 FFC007FF80486C48D9F00F13E03D1C3E1F81F83F03F0DA3C00EB780126383F78D9FCF07F 4AEBFDE000704990387DC0004AEB7F804A91C7FC91C700FE1301485A017E5CA212004949 48495AA34E5A4848495AA24E5AA24848495A95381F80E0A34848494890383F01C0A39538 3E03804848495AF10700190EF01E1E484849C7EA1FFC000F6E6E5A6CC7000EEC03E04326 7EA449>I<90390F8003F090391FE01FFC496C487E903970F87C1F9238F00F80903AE0FD C007C0DAFF8013E04848EB00035C4A14F0A2380381F8A3D800011407495AA44948EB0FE0 A317C04948131F1780A2EE3F00495A6E137E167C5E496C485A4B5A6E485A9138781F8090 267E3FFFC7FCEC1FFCEC07E091C9FC5BA4485AA4485AA3387FFFC0B5FC7E2C3583A42A> 112 D<02FC13C0903803FF01010F138390391F83C78090383E01EF9038FC00FF4848137F 491400485A000780485A157E485AA2123F90C75A5AA300FE495AA448495AA44A5AA2140F 007C131F007E495A003E137F14FF381F83EF390FFF9F800003131FEA00FC13004AC7FCA4 147EA45CA2130190387FFFF0A322357DA425>I<14FF010313C0010F13F090381F80F890 383E003849133C49137C4913FC00011301A215F80003EB00F06D13007F3801FFC014FC6C 13FF15806D13C0011F13E013079038003FF0140F1403121E123F5A4814E0A215C0481307 00F814800070EB0F000078133E003F13FC6CB45A000713E0000190C7FC1E267CA427> 115 D<13F8D803FE1438486C147CD80F0F14FC000E7F121C12384B5AEA701FA348484848 5AA3EA007E4B5A5BA34848495AA44848495AEE81C0A392383F0380A2157FA29238FF0700 00015B9039F8039F0E3900FC0F1F90397FFE0FFC90391FFC07F8903907F001F02A267EA4 30>117 D<01F8EB0380D801FEEB07C0D807FFEB0FE0D80F0F14F0000E1380121C003814 071503D8701F1301A216E038E03F001500A2D8007E130116C05BA34848EB0380A3ED0700 485A1506150EA25DA25D5D12016D5B0000EB03C090387E07806DB4C7FCEB1FFCEB07F024 267EA428>I<01F816E0D801FE9138E001F0D807FF903901F003F8D80F0F010314FC000E 1380121C00381601923807E000D8701F167CA21878484848485A1838A2D8007E16784B48 13705BA3484849C712E0A3EF01C04848137EA2EF0380A3EF0700A203FE130E00015E6D48 7E0000D9039F5B903A7E0F0FC0F0903A3FFE07FFE06D486C5B902703F8007FC7FC36267E A43B>I<90390FC007E090393FF00FF890397FF83FFC9039F07C783C3A01C03EF03E3A03 801FE07ED80700EBC0FE000E14C115815AED80FC4890383F00701600A2C7FC147EA45CA4 495A1638A2121C267E03F0137012FF16E0130700FEEC01C0D8FC0FEB03803AF81EF80700 39783C7C1E397FF83FFC393FE01FF8390FC007E027267DA42F>I<13F8D801FE1470D807 FF14F8D80F0F1301000E1380121C1238ED03F0EA701FA33AE03F0007E0A3EA007EED0FC0 5BA34848EB1F80A44848EB3F00A4157EA315FE4A5A00011303EBF8073800FC1F90387FFF F8EB3FF9EB0FE1EB00014A5AA2000E495A121F486C485A127F4A5A010090C7FC007E133E 007C5B383801F8383E07F0381FFFC06C90C8FCEA01FC25367EA429>I<D901E013E0EB07 F890391FFC01C090393FFE0380A290397FFF8F009038F81FFE9038E007FC3801C0001538 495BC85A4A5A4A5A4AC7FC140E5C5C14F0495AEB038049C8FC130E5B4913075B495B4848 130E4848131ED807F05B01FE137C390FFF81F8391F1FFFF0D83C075BD838035B486C5B48 6C90C7FC147C23267DA427>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FG cmr8 8 58 /FG 58 123 df<EA03E012FFA3120F1207B3A4EAFFFEA30F1E7F9D13>16 D<EA01E0EA03F0A21207120FEA1FE01380EA3F00127E127C12F012600C0C72AD23>19 D<00C013C0EAF003EAFC0F387F3F80381FFE006C5AEA03F06C5A120878AA23>I<EB01F0 EB07FC497EEB1F0EEB3E07133C90387C0380A213FC13F8A213FC4AC8FCA2140E5C143CEB 7E780270EB7FFF5CEB7FC06D48EB1FF091C7EA07C06E1400A2496C130E01FF5C3801EFE0 D803875C00076D5B380F03F8D81F015C003E6D485A387E00FE91387F038000FE4AC7FCEC 3F8EEC1FCEEC0FFC6E48130E007F13036E6C131E6C6C486C131C001F90390FFF803C3B0F E07E1FE0F83B07FFFC0FFFF06CD9F00313E03B007F80007F8030307DAE37>38 D<1307130F131E133C1378137013F0EA01E0120313C012071380120F13005AA2121E123E A35AA612FC5AAD7E127CA67EA3121E121FA27E1380120713C0120313E01201EA00F01370 1378133C131E130F130710437AB11B>40 D<126012F012787E7E120E120FEA078013C012 0313E0120113F0120013F8A21378137CA3133EA6133F131FAD133F133EA6137CA3137813 F8A213F0120113E0120313C012071380EA0F00120E121E5A5A5A126010437CB11B>I<12 3C127EB4FCA21380A2127F123F1203A312071300A2120EA25A123C12385A122009157A87 14>44 D<123C127E12FFA4127E123C08087A8714>46 D<15C01401A2EC0380A3EC0700A2 140EA35CA35CA35CA35CA2495AA3495AA349C7FCA3130EA25BA35BA35BA35BA3485AA248 5AA348C8FCA3120EA35AA35AA25AA35AA25A1A437CB123>I<EB3FC0EBFFF0000313FC38 07F0FE380FC03F497E391F000F80A24814C0003E1307007E14E0A500FE14F0B0007E14E0 A46CEB0FC0A36C1480390F801F006D5A3807F0FE6CB45AC613F0EB3FC01C2D7DAB23>I< 130E131E137EEA01FE12FFA2EAFE7E1200B3AF13FF007F13FFA3182C7BAB23>I<EB7F80 3801FFF0000713FC380F81FE381E007F0038EB3F8048EB1FC0007814E000FC130F7E6C14 F01407A2127E123CC7120FA215E0A2EC1FC01580143F1500147E5C495A495A14C0495A49 C7FC131E5B4913705B485A484813E048C7FC120E001FB5FC5A5AB612C0A31C2C7DAB23> I<EB3F803801FFF04813FC3807C0FE380E007F001EEB3F80123F9038801FC0A4381F003F 000E1480C7FCA2EC7F00147E5CEB03F8EBFFF014C014F0EB00FC147E80EC1F8015C0EC0F E0A215F0A2123C127EB4FCA215E0A248EB1FC0127C0078EB3F806C1400381F80FE3807FF FC6C13F038007F801C2D7DAB23>I<140F5CA25C5CA25C5BA25BEB07BF143F130F131E13 1C1338137813F013E01201EA03C013801207EA0F00120E121E5A123812785AB612FCA3C7 EA3F00A8EC7F8090381FFFFCA31E2D7EAC23>I<EB03F8EB0FFEEB3FFF90387E0780EBF8 033901E00FC03803C01F1207EA0F80121F9038000F804890C7FCA3127EA2EB1FF038FE3F F8EB7FFEEBE03F6C487E9038800F80010013C0EC07E0A34814F0A4127EA4003E14E0123F A26CEB0FC01580EA0F803907C01F003803F07E6CB45A38007FF0EB1FC01C2D7DAB23>54 D<EB3F80EBFFF0487F3807E07C380F803E001F7F9038000F805A007E14C0A2140700FE14 E0A415F0A4007E130FA37E6C131F380F803FEBC0773807FFE7000113C76CEB87E0EB0007 A3EC0FC0A2001F1480383F801F1500A2143E495A001C5B380F03F06CB45A6C1380C648C7 FC1C2D7DAB23>57 D<EC03C0A24A7EA34A7EA34A7EA3EC39FCA2EC79FE1470A2ECF0FF4A 7EA249486C7EA349486C7EA2010780EC000FA24980010E1307A2011FB57EA24980903838 0001A201788001701300A249147FA30001ED3F801203D80FF0EC7FC0D8FFFE0107B5FCA3 302F7EAE35>65 D<B612FCEDFF8016E03A03FC000FF80001EC03FC6F7E6F7E821780A617 005E5E4B5AED07F8ED1FF090B612C05E16F09039FC0007F8ED01FE6F7EEE7F80163F17C0 161F17E0A6EE3FC0A2EE7F80EEFF005D0003EC07FCB75A16E093C7FC2B2D7EAC32>I<DA 1FF013C09138FFFE010107EBFF8390390FF807C390393FC001E749C7127F01FC143F4848 141F4848140F00071507485A491403121F123F491401A2127F90C8FC93C7FC5AA97EA26D EC01C0123FA27F121F000FED03807F6C6CEC070012036C6C140E6C6C5C017F5CD93FC013 F090390FF807E06DB51280010049C7FCEC1FF02A2F7CAD33>I<B712FEA33903FC000300 01EC007F828282A282A392381C0380A493C7FC153CA215FC90B5FCA3EBFC00153CA2151C 17E0A3EE01C01500A31603A217801607160F161F163F0003EC01FFB81200A32B2D7EAC30 >69 D<B712FCA33903FC00030001EC00FE163EA2161EA2160EA316071538A31600A21578 A2EC01F890B5FCA3EBFC01EC0078A21538A592C7FCA9487EB512FCA3282D7EAC2E>I<DA 1FF013C09138FFFE010107EBFF8390390FF807C390393FC001E749C7127F01FC143F4848 141F4848140F00071507485A491403121F123F491401A2127F90C8FC93C7FC5AA892383F FFFE7EA26D9038003FC0003F151FA27F121F120F7F6C7E12036C7ED800FE143F137FD93F C013F790390FF803E36DB512C101001400DA1FF813002F2F7CAD37>I<B512F8A33803FE 006C5AB3B3487EB512F8A3152D7EAC19>73 D<90387FFFF8A30100130080B3AC123C127E B4FCA2147E4813FE007C5B387801F8383E07F06CB45A00075BD801FEC7FC1D2E7EAC24> I<B500F8EB7FFFA3D803FEC7EA3FF06C48EC1F80041EC7FC5E5E5E4B5A4B5A4B5A4BC8FC 151C5D5D4A5A4A5A4A7E140F4A7E4A7EEC7BFC14E19038FDC0FE9038FF80FF4A7E496D7E 496D7E82150F6F7E8215036F7E6F7E8282707E83707E486C4A7EB5D8F801B51280A3312D 7EAC37>I<B512FCA3D803FEC8FC6C5AB3A5161CA41638A41678A216F815011503ED07F0 0003143FB7FCA3262D7EAC2C>I<D8FFFE92381FFFC0A3D803FF92383FF0006C5FD9DF80 1477A3D9CFC014E7A2D9C7E0EB01C7A3D9C3F0EB0387A2D9C1F8EB0707A3D9C0FC130EA3 027E131CA26E1338A391381F8070A291380FC0E0A3913807E1C0A2913803F380A3913801 FF00A36E5A487ED80FF8017C497EB500800103B512C0A215383A2D7DAC41>I<D8FFFC49 B5FC7FA2D801FF9038001FF06EEB07C06EEB038013DFEBCFE08013C7EBC3F8EBC1FC8013 C0147F1580143FEC1FC0EC0FE015F01407EC03F815FCEC01FE1400157F1683153FED1FC3 ED0FE316F31507ED03FB16FF8181167FA2163F161F487ED80FF8140FB56C13071603A230 2D7EAC35>I<EC3FF0903801FFFE01076D7E90391FE01FE090393F8007F09039FE0001FC 48486D7E4848147F4848EC3F8049141F000F16C04848EC0FE0A24848EC07F0A2007F16F8 A290C81203A24816FCAA6C6CEC07F8A3003F16F06D140F001F16E0A26C6CEC1FC06D143F 000716806C6CEC7F006C6C14FE6C6C495A90397F8007F890391FF03FE00107B512800101 49C7FC9038003FF02E2F7CAD37>I<B612F8EDFF8016E03A03FC001FF00001EC03F86F7E 6F7E82821780A717005E5E4B5A4B5AED1FF090B65A168003F8C7FC01FCC9FCB0487EB512 F8A3292D7EAC30>I<B612E015FE6F7E3A03FC003FE00001EC07F06F7E6F7E82150082A6 5E15015E4B5A4B5AED3FE090B612804BC8FCA29038FC007FED1F806F7E82150782A582A4 EF038016FC1503486C903901FE0700B500F86D5A9238007FFE705AC9EA07F0312E7EAC34 >82 D<90383F80303901FFF07048EBFCF0380FC07E381F000F001E1307481303007C1301 127800F81300A21570A27EA26C1400127F7FEA3FF8EBFF806C13F86C13FE6C7F6C14C0C6 14E0130F010013F0EC0FF814031401EC00FCA20060147C12E0A46C1478A26C14F07E6CEB 01E039FF8003C039F7F00F8000F1B5120038E07FFE38C00FF01E2F7CAD27>I<007FB712 F8A39039800FE007D87E00140000781678A20070163800F0163CA348161CA5C71500B3A7 4A7E011FB512F0A32E2D7EAC33>I<B500E090381FFFC0A3D803FEC73803FC006C48EC01 F05F7F00005E6D14036D5DA26D6C49C7FCA26E5B011F140EA26D6C5BA26E133C01071438 A26D6C5BA26E13F001015CA26D6C485AA2ECFF03027F5BA2DA3F87C8FCA215CFEC1FCEA2 EC0FFCA36E5AA26E5AA36E5AA2322E7FAC35>86 D<EB7F803803FFE0000F13F848C67E14 3E383F803FEC1F80A2391F000FC0120EC7FCA3EB07FF137F3803FF8F3807F80FEA1FE0EA 3F8013005A00FE14C7A4141F127F1477393FC1E7FE381FFFC30007EB81FC3901FC00F020 207E9E23>97 D<EA03E012FFA3120F1207AB147F9038E3FFE001E77F9038FF01F89038FC 007C497F49133F49EB1F80A2ED0FC0A216E0A816C0A2151F1680A26DEB3F006D137E01DC 5B90388F03F8903887FFF0010313C0C76CC7FC232F7FAD27>I<EB1FE0EB7FF83801FFFE 3803F01FEA07E0390FC03F80EA1F80130048EB1F0048130E91C7FC127E12FEA8127E127F A26CEB01C01380001FEB0380EA0FC03907E007003803F81E3801FFFC6C6C5AEB1FC01A20 7E9E1F>I<157CEC1FFCA314011400ABEB1FE0EB7FF83801FFFE3803F81F3807E007380F C001381F800048C7FCA25A127EA212FEA7127EA37EA2381F8001000F13036C6C487E3A03 F03EFFE03801FFFC6C13F090391FC0F800232F7EAD27>I<EB1F80EBFFF0487F3803F0FC 3807C03E380F803F48487E481480140F127E15C0A212FEB6FCA348C8FCA4127EA2127F6C EB01C0A2391F800380EA0FC03907E007003803F81E3801FFFC6C6C5AEB1FC01A207E9E1F >I<EB01F8EB07FEEB1FFF90383F1F80EB7C3F13F81201EC1F003803F00E91C7FCA9B512 E0A3D803F0C7FCB3A47F387FFFC0A3192F7FAE16>I<90383F80F89038FFE3FC0003EBFF FED807E0133E390F803E1C1508391F001F00A2481480A56C1400A2380F803EA23807E0FC EBFFF8000C13E0EB3F80001CC8FCA2121E121F380FFFF814FF6C14C015E04814F0391F00 07F8003C1301007CEB00FC48147CA5007C14F86CEB01F06CEB03E0390FE01FC06CB51280 0001EBFE0038003FF01F2D7E9D23>I<EA03E012FFA3120F1207ABEC3F80ECFFE001E37F 9038E781F89038EE00FC13FC49137E5BA25BB2B5380FFFF0A3242E7FAD27>I<EA0780EA 0FC0EA1FE0A4EA0FC0EA0780C7FCA8EA03E012FFA3120F1207B3A4EAFFFEA30F2E7FAD13 >I<EA03E012FFA3120F1207ACEC1FFFA3EC0FF015C092C7FC141E5C5C14E0EBE3C0EBE7 E013EFEBFFF0EBFDF8EBF8FCEBE07C147E806E7E140F816E7E6E7E8181B5380FFFC0A322 2E7FAD25>107 D<EA03E012FFA3120F1207B3B3A2B5FCA3102E7FAD13>I<2607E07FEB0F E03BFFE1FFC03FF801E36D487E903AE783F0F07E3B0FEE01F9C03F3B07F800FB001F03FF 1480495BA2495BB2B53A1FFFE3FFFCA3361E7E9D3B>I<3903E03F8000FFEBFFE001E37F 9038E781F8390FEE00FCEA07FC49137E5BA25BB2B5380FFFF0A3241E7F9D27>I<EB1FE0 EB7FF83801FFFE3803F03F3907C00F80390F8007C0391F0003E04814F0A2007EEB01F8A3 00FE14FCA9007E14F8A26CEB03F0A26C14E0EB8007390FC00FC03907F03F803901FFFE00 38007FF8EB1FE01E207E9E23>I<3803E07F39FFE3FFE001E77F9038FF03F8390FFC00FC 6C48137E497F491480151F16C0A2ED0FE0A816C0151FA21680153F6DEB7F006D137E6D5B 9038EF03F89038E7FFF001E313C0D9E07FC7FC91C8FCA9B5FCA3232B7F9D27>I<3807C1 F038FFC7FCEBCFFEEBDE7FEA0FD8EA07F8EBF03E141C14005BB17FB51280A3181E7E9D1C >114 D<3801FE183807FFB8001F13F8EA3F01EA7C000078137800F81338A37E6C13006C 7EEA7FFC383FFF806C13E06C13F06C13F8C613FC1307EB00FE0060137E00E0133EA27EA2 6C133C147C6C137838FF01F038F7FFE000E313C000C0130017207E9E1C>I<13E0A41201 A31203A21207120F121FB512F0A33807E000AE1438A70003137013F03801F8E0EA00FFEB 7FC0EB1F00152A7FA81B>I<D803E0133E00FFEB0FFEA3000F13000007147EB115FEA300 0313019038F0037F2601F80E13F03800FFFCEB7FF890391FE07C00241F7F9D27>I<3AFF FE03FFC0A33A07F000FE00157800031470A26C6C5BA2EBFC0100005CA290387E0380A2EB 7F07013F90C7FCA2148FEB1F8EA2EB0FDCA214FC6D5AA26D5AA36D5AA2221E7F9C25>I< 3BFFFE7FFE0FFFA33B0FF007F003F83B07E003E001E015F0D803F015C0A29039F807F803 00011680A29039FC0FFC070000D90E7C1300A290397E1E7E0EEC1C3E153FD93F3C5BEC38 1F169C90391FF00FB8A216F86D486C5AA36D486C5AA36D486C5A301E7F9C33>I<3AFFFE 0FFF80A33A07F807F8000003EB03E0D801FC138000001307D97E0FC7FCEB7F1EEB3FBCEB 1FB8EB0FF85C1307130380497E497EEB1E7EEB1C3F90383C1F8001787FEBF00F48486C7E 00036D7E390FF007F83AFFF80FFFC0A3221D7F9C25>I<3AFFFE03FFC0A33A07F000FE00 157800031470A26C6C5BA2EBFC0100005CEBFE03017E5BA26D48C7FCA2148FEB1F8EA2EB 0FDCA214FC6D5AA26D5AA36D5AA25CA213035C1238D87C07C8FC12FE130E131E485AEA78 78EA7FF06C5AEA0F80222B7F9C25>I<003FB51280A39038007F00003C137E00385BEA78 01495A00705B495A130F495A00005B133F49C7FC9038FE038013FC1201EA03F813F03807 E007120FD81FC01300495A48485A48137FB6FCA3191D7E9C1F>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FH cmsy6 6 3 /FH 3 123 df<136013F0A30060136000F013F0EAFC63EAFE67383FFFC03807FE00EA01 F8EA07FE383FFFC038FE67F0EAFC63EAF0F00060136000001300A3136014157B9620>3 D<13E0487EA76C5AA53878E3C0B512E0A33878E3C03800E000A3487EB36C5AA7132F7CA3 1D>121 D<13E0487EA56C5AA33878E3C0B512E0A33878E3C03800E000A3487EA56C5A90 C7FC13E0487EA56C5AA33878E3C0B512E0A33878E3C03800E000A3487EA56C5A132F7CA3 1D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FI cmss10 10 14 /FI 14 119 df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ndDVIPSBitmapFont %DVIPSBitmapFont: FJ cmsy7 7 14 /FJ 14 122 df<B712FEA327037A8F34>0 D<1238127C12FEA3127C123807077A9114>I< 0060140600F0140E0078141E6C143C6C14786C14F039078001E03903C003C03901E00780 3900F00F00EB781E6D5A6D5A6D5A6D5A6D5A497E497EEB1E78497E497E497E3901E00780 3903C003C039078001E048C712F0001E147848143C48141E48140E006014061F1F769D34 >I<1338A50060130C00F8133E00FC137E00FE13FE383FBBF83807FFC000011300EA007C 48B4FC000713C0383FBBF838FE38FE00FC137E00F8133E0060130C00001300A517197B9A 22>I<1303497E497E497EEB3CF0EB7878497E48487E48487E3907800780390F0003C000 1EEB01E048EB00F0481478481438007814786C14F06CEB01E06CEB03C039078007803903 C00F003801E01E6C6C5AEB78786D5AEB1FE06D5A6D5A6DC7FC1D1D7E9C22>5 D<EC7FC0903803FFF8010F13FE90393F803F809039FC0007E0D801F0EB01F0D803C0EB00 78000781486C147ED80EF014FED81C78EB01E76DEB03C7486C90380783806DEB0F033B70 07801E01C0903803C03C903801E0783BE000F0F000E0EC79E0EC3FC06E5A6EC7FC4A7E4A 7EEC79E0ECF0F03B7001E07801C0903803C03C903807801E3B380F000F0380011EEB0783 6C48903803C70049EB01E76C48EB00FED80FE0147E6C48143C00035DD801F0495AD800FC EB07E090393F803F8090260FFFFEC7FC010313F89038007FC02B2B7CA334>10 D<137F3801FFC0000713F0487F487F487FA2487FA2B61280A76C1400A26C5BA26C5B6C5B 6C5B000113C06C6CC7FC19197C9A22>15 D<17601770A317781738A28383170F83EF03C0 717EEF00F8007FB9FCBA12806C1800CB12F8EF01E04D5A4DC7FC5F170E5F5FA217781770 A31760391F7C9D42>33 D<13021307B3AF00C0141800F814F800FE1303003FEB07E03907 870F003801C71C3800E738EB7770EB3FE06D5AA26D5AA26DC7FCA313021D337EA722>35 D<1608161C041FEB018093380FE00F0403B512001600EF0FFEEF007E18FE4D5AEF039CEF 071C170E173C177817F0EE01E0EE03C04CC67E160E5E04787F5E4B487F4B4890C7FC4B5A 030EC9FC5D5D15F04A5A4A5A4A5A4ACAFC141C5C5C495A495A495A49CBFC131E13385B5B EA03C0485A48CCFC121E5A12705A124039357CA942>37 D<124012E012787E7E7E6C7E6C 7E6C7EEA0070133C7F7F6D7E6D7E6D7E6D7E1438141E806E7E6E7E6E7E6E7E1578151C15 0F6F7E6F7E6F6C13036F6C5B167870130E160EEE0780706C5AEE01E0EE00F01778173C17 1E1707EF03DCEF01FC717E187EEF0FFE94B5FC160393390FE00F8093381F0001041C90C7 FC160839357CA742>I<13E0EA01F0EA03F8A3EA07F0A313E0A2120F13C0A3EA1F80A213 00A25A123EA35AA3127812F8A25A12100D1E7D9F13>48 D<387FFF80B512F06C13FCC712 7FEC0F80EC03C0EC01E0EC00F015781538151CA2150EA31507A3B7FCA3C81207A3150EA3 151CA21538157815F0EC01E0EC03C0EC0F80EC7F00387FFFFCB512F06C138020277AA12D >51 D<137013F8A71370A6387C71F0B512F8A3387C71F038007000A413F8B3A41370A815 357CA81E>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FK cmsy10 10 25 /FK 25 115 df<007FB81280B912C0A26C17803204799641>0 D<121E123FEA7F80EAFF C0A4EA7F80EA3F00121E0A0A7A9917>I<0060150600F0150F6C151F007C153E6C157C6C 15F86C6CEB01F06C6CEB03E06C6CEB07C06C6CEB0F806C6CEB1F00017C133E6D5B6D5B90 380F81F0903807C3E0903803E7C06DB45A6D90C7FC147EA214FF497F903803E7C0903807 C3E090380F81F049C67E013E137C497F497F4848EB0F804848EB07C04848EB03E04848EB 01F048C812F8003E157C48153E48151F48150F00601506282874A841>I<1430147814FC 497E497E903807CF8090380F87C090381F03E090383E01F0496C7E49137C48487F48487F 4848EB0F804848EB07C048C7EA03E0003EEC01F048EC00F848157CA2007C15F86CEC01F0 6CEC03E06C6CEB07C06C6CEB0F806C6CEB1F006C6C133E6C6C5B017C5B6D485A6D485A90 380F87C0903807CF806DB4C7FC6D5A6D5A1478143026267EA72B>5 D<EC03FF023F13F091B512FC903903FC00FFD90FC0EB0FC0013FC7EA03F0017CEC00F801 F0153C484881486C151F486CED3F80013C157BD80E1EEDF1C06DEC01E1486C6C903803C0 E06D6CEB0780486C6C90380F00706D6C131E4801784913386E5B6E5B6E485A4890260783 C0131C913803C780DA01EFC7FCEC00FE157CA215FEEC01EF913803C78091380783C00070 90260F01E0133891381E00F04A13784A7F6C496D137049487F6C484890380780E04948EB 03C06C48C73801E1C0011EEC00F16C48ED7B8001F8153F6C48ED1F006C48151E6C6C5D01 7C15F8013FEC03F0D90FC0EB0FC0D903FC01FFC7FC0100B512FC023F13F0020390C8FC36 367BAF41>10 D<EB0FE0EB7FFC497E0003EBFF803907F01FC0390FC007E0391F0001F000 1E1300481478007C147C0078143CA248141EA70078143CA2007C147C003C14786C14F000 1F1301390FC007E03907F01FC06CB51280C6EBFE006D5AEB0FE01F1F7BA42A>14 D<020FB6128091B712C01303010F1680D91FF0C9FC017FCAFC13FC485AEA03E0485A5B48 CBFC5A121E5AA25AA45AAA1278A47EA27E121F7E6C7E7F6C7EEA01F86C7E137FEB1FF06D B71280010316C01300020F158091CAFCAE001FB812804817C0A26C1780324479B441>18 D<EF0180EF07C0171FEF7F80933801FE00EE07F8EE1FE0EE7F80DB01FEC7FCED07F8ED1F E0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB07F8EB1FE0EB7F80D801FECA FCEA07F8EA1FE0EA7F8000FECBFCA2EA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0EB07 F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8ED01FE9238007F 80EE1FE0EE07F8EE01FE9338007F80EF1FC01707EF018094C7FCAE007FB81280B912C0A2 6C1780324479B441>20 D<126012F812FEEA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0 EB07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8ED01FE9238 007F80EE1FE0EE07F8EE01FE9338007F80EF1FC0A2EF7F80933801FE00EE07F8EE1FE0EE 7F80DB01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB 07F8EB1FE0EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFC12F81260CCFCAE007FB8 1280B912C0A26C1780324479B441>I<D93F801508D9FFF0150C00036D151C4813FE487F 4814C09038C07FE0273F000FF01438003CEB07FC48D901FE147800706D6C6C13F092383F C0034891391FF80FE06FB5FC030314C06F14806F6C13000060ED3FFC0040ED07F036137B 9D41>24 D<181C181EA384A3727EA2727EA2727E85180019788585F11F80F107C0F103F0 007FBA12FCBCFCA26C19FCCCEA03F0F107C0F11F80F11E006161611801614E5AA24E5AA2 4EC7FCA3181EA3181C482C7BAA53>33 D<1738173CA283A283717EA2717E717E84170018 78007FB812FCB97E727E6C84CBEA03E0F001F8F0007EF13F80F10FE0F107F8F101FFA2F1 07F8F10FE0F13F80F17E00F001F8F003E0007FB95ABA5A4EC7FC6C5FCB1278601701604D 5A4D5AA24DC8FC171EA25FA2173848307BAC53>41 D<DA0380141C6F143C4A4880A24AC8 7EA2021E6F7EA24A6F7E027C82027815014A6F7E4948167849B812FC498349834984013E CAEA07C049717E4848EF01F84848717ED80FC0183FD83F80F01FC0B4CCEA0FF0A2D83F80 F01FC0D80FC0F03F00D803F018FC6C6C4D5AD8007CEF03E06D4D5A6DB95A6D95C7FC6D5F 6D5FD901E0C912786D6C5E02784B5A027C1503023C5E6E4B5AA26E4BC8FCA26E6C141EA2 6E6C5C4B141C4C307DAC53>44 D<91380FFFFE91B6FC1303010F14FED93FF0C7FC49C8FC 13FCEA01F0485A485A5B48C9FC5A121E5AA25AA45AA3B712FE16FFA216FE00F0C9FCA312 78A47EA27E121F7E6C7E7F6C7E6C7EEA00FC137FEB3FF0010FB512FE010314FF1300020F 13FE283279AD37>50 D<387FFFF0B6FC15C06C14F0C7EA0FFCEC00FE153FED0F80ED07C0 ED03E01501ED00F016F81678163CA2161EA4160FA3007FB7FCB8FCA27EC9120FA3161EA4 163CA2167816F816F0ED01E01503ED07C0ED0F80ED3F0015FEEC0FFC007FB512F0B612C0 92C7FC6C13F0283279AD37>I<126012F0AD12F812FCA212F812F0AD126006207BA400> 55 D<0060161800F0163CA200781678A36C16F0A36CED01E0A26CED03C0A36C6CEC0780 A36C6CEC0F00A26C6C141E90B612FEA26C5DA201F0C7123C01785CA26D5CA36D495AA36D 495AA26D6C485AA36D6C48C7FCA3903801E01EA26D6C5AA3EC7878A36E5AA2EC1FE0A36E 5AA36E5AA26EC8FC2E3C80B92F>I<007FB612F0B712F8A27EC91278B3A5003FB612F85A A27EC91278B3A5007FB612F8B7FCA26C15F0253A7CB92E>I<EE01FCEE0FFEEE3FFF93B5 FC030314805DED1F03ED3E01157CEDFC004A4814004A5A5F4A485B020F14F09238C001C0 021F90C8FC5D143F92C9FC5CA214FEA213015CA21303A25C1307A35C130FA25CA2131FA2 5C133FA25CA249CAFCA2017E16E001FE15034915070001EE1FC0EBFFFC48D9FFC0EB3F80 03FC1400489138FFE03E48EDFFFC17F0D81F035D263C003F148048010349C7FC00E09038 001FF0333D7EBA39>76 D<14034A7EA24A7EA24A7EA3EC3CF0A2EC7878A24A7EA349487E A249487EA249486C7EA249486C7EA3011E6D7EA2496D7EA2491478A34980A2484880A248 4880A24848EC0780A348C8EA03C0A2001EED01E0A248ED00F0A3481678A248163CA20060 16182E347CB137>94 D<1606160FB3A8007FB7FCB8FCA27EC9120FB3A81606283A7BB933 >97 D<15FE1407141FEC7FC0ECFE00495AEB03F0A2495AB3A8495AA2495A49C7FC13FEEA 07FCEAFFF0138013F0EA07FCC67E133F6D7E6D7EA26D7EB3A86D7EA2EB01FC6D7EEC7FC0 EC1FFE140714001F537BBD2A>102 D<127EEAFFE013F8EA07FEC67EEB3F806D7E130F6D 7EB3A86D7EA26D7E6D7E147FEC3FC0EC0FFE1403140FEC3FC0EC7F0014FC495A495AA249 5AB3A8495A131F495A01FFC7FCEA07FEEAFFF813E0007EC8FC1F537BBD2A>I<126012F0 B3B3B3B3A91260045377BD17>106 D<BA12F0A26C18E0A26C18C0A26C188001F0C91203 18076C6C1700606C6C160E181E6C6C161C183C6C6C163818786C6D157018F06D6C5D1701 6D6C5D17036D6C5D17076D6C92C7FC5F6D6C140EA26D6C5CA201015D806D5D81027F5C81 1601DA3FE05B1603DA1FF05B1607DA0FF890C8FC5E913807FC0E161E913803FE1C163C91 3801FF3816786E5BA26F5AA26F5AA26F5AA26FC9FCA23C3C7CB845>114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FL cmr10 10 85 /FL 85 124 df<EC0FFE91387FFFC00103B512F890390FFC07FE90391FE000FFD97F80EB 3FC049C76C7ED801FCEC07F000038248486E7E491401000F8248486E7EA2003F1780A249 157F007F17C0A9003F17806D15FFA2001F1700A26C6C4A5AA200075EA26C6C4A5AA20001 5E6D140700005E017C5D017E140F013E5DA26D4AC7FC00E017E06D141E0070EE01C06D6C 133CA2010314380078160300386D01781380D83FFFEC7FFFA46C170082333B7CBA3C>10 D<DA07FC13FC91393FFF07FF49B5009F1380903B03FC07FF8FC0903B0FE003FE0FE0903A 1FC007FC1F90383F800FD97F0013F8017EED0FC001FE903907F007804992C7FC1201ACB8 12F8A32801FC0007F0C7FCB3AB486C497E267FFFE0B512F0A3333B7FBA30>I<EC07F8EC 3FFE49B57E903903FC07C090390FE001E090381FC0034948487E90387F000F137E13FE49 6D5A00016E5A6F5A92C8FCA9ED07F0B7FCA33901FC001F1507B3AA486C497E267FFFE0B5 12C0A32A3B7FBA2E>I<EC07FC91387FFF7049B512F0903803FC0790380FE00FEB1FC0EB 3F005B017E130713FE5B1201ACB7FCA33901FC0007B3AB486C497E267FFFF1B512C0A32A 3B7FBA2E>I<DA07FCEB0FF0DA3FFFEB7FFC49B50083B5FC903C03FC07C7F80F80903C0F E000FFC003C0494848EB800749484849487E49484848131F017E5C13FE494A6D5A000102 036E5A72C7FC95C8FCA9F00FE0BAFCA33C01FC0003F8003F180FB3AA486C496C497E267F FFF0B500E3B51280A3413B7FBA45>I<137C137E13FE1201120313FCEA07F8EA0FF013E0 EA1FC0EA3F00127E127C5A12600F0F6FB92A>19 D<B612F8A41D047AB02A>22 D<001E130F003FEB1F80397F803FC039FFC07FE0A201E013F0A2007F133F003F131F001E EB0F7000001300A4484813E0A339038001C0A23907000380A2000EEB070048130E003C13 1E0038131C001013081C1A7DB92A>34 D<121E123FEA7F80EAFFC0A213E0A2127F123F12 1E1200A4EA01C0A3EA0380A2EA0700A2120E5A123C123812100B1A7AB917>39 D<14E01301EB03C0EB0780EB0F00131EA25B5B13F85B12015B12035B1207A2485AA2121F 90C7FCA25AA2123EA2127EA5127C12FCB2127C127EA5123EA2123FA27EA27F120FA26C7E A212037F12017F12007F13787F7FA27FEB0780EB03C0EB01E01300135278BD20>I<1260 12F012787E7E7EA26C7E6C7E7F12017F12007F1378137CA27FA2133F7FA21480A2130FA2 14C0A5130714E0B214C0130FA51480A2131FA21400A25B133EA25BA2137813F85B12015B 12035B485A48C7FCA2121E5A5A5A126013527CBD20>I<15301578B3A6007FB812F8B912 FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D<121E123FEA7F80EAFFC0A213E0A2 127F123F121E1200A4EA01C0A3EA0380A2EA0700A2120E5A123C123812100B1A7A8917> I<B512FCA616067F941C>I<121E123FEA7F80EAFFC0A4EA7F80EA3F00121E0A0A7A8917> I<EB03F8EB1FFF017F13C09038FE0FE03901F803F048486C7E48486C7E4848137EA24848 7FA2003F1580A290C7121F4815C0A64815E0B36C15C0A56C6CEB3F80A3001F1500A26C6C 137EA26C6C5B6C6C485A6C6C485A3900FE0FE090387FFFC0011F90C7FCEB03F8233A7DB7 2A>48 D<EB01C013031307131F13FFB5FCA2131F1200B3B3A8497E007FB512F0A31C3879 B72A>I<EB0FF0EB7FFE48B57E3903E03FC03907800FE0390E0007F0486D7E48806E7E5A 6E7E127CB4FC16807F157FA26CC7FCA2001C14FFC8FC1600A25C5D5D14035D4A5A4A5A5D 4A5A4AC7FC143E5C5C495A495A495A5C49C8FC011EEB03805B5B491307484814005B485A 48C75A48B6FC5A5A485CB6FCA321387CB72A>I<EB07F8EB3FFF4913C03901F80FE03903 E003F0D807807F496C7E488013C0486C6C7EA4120F495AD803805BC7FCA25D14035D4A5A 5D4A5AEC7F80D91FFEC7FC5CECFF809038000FE0EC03F06E7E6E7E81157F1680A2ED3FC0 A216E0A2123E127F487EA316C090C7FC48147F007C158012706CECFF006C5C000F495A39 07C003F83903F80FF06CB512C06C6C90C7FCEB07F8233A7DB72A>I<157815F8A2140114 03A21407A2140F141FA2143F147B147314F3EB01E314C31303EB07831403130F131E131C 133C1378137013F0EA01E013C012031380EA07005A120E121E5A123812785AB712F8A3C7 3803F800AB4A7E0103B512F8A325397EB82A>I<0004140C000F143C9038F003FC90B55A 5D5D158092C7FC14FC000E13F090C9FCABEB07F8EB1FFE90387FFF809038F80FC0390FE0 07E090388003F0496C7E000E6D7E1206C87EA2157FA31680A31218123E127F5AA316005A 00785C00705CA26C495A5D6C495A6C495A6C6C485A3903E03F806CB5C7FC38007FFCEB1F E0213A7CB72A>I<EC3FC0903801FFF0010713FC90380FE03E90381F000F013E5B49EB3F 8049137F485A485A120749EB3F00000F141E001F91C7FC5BA2123FA3387F0020EB03FF49 13C0497F39FF1C03F090383000F849137C157E497FA2491480151F16C0A290C7FC16E0A4 7EA57E6D14C0A2121FED3F80120F6D14000007147E6C6C137C6D5B6C6C485A3900FE07E0 90383FFFC06D90C7FCEB03FC233A7DB72A>I<1238123C123F90B612E0A316C0481580A2 16000078C7120E00705CA25D00F05C5A5D4A5AC7FC4A5A4AC7FC140EA25C143C14381478 147014F0A2495AA21303A2495AA2130FA3131F5CA3133FA5137FA96DC8FC131E233B7BB8 2A>I<EB03F8EB1FFF4913C09038FC07E03901F001F03903C000F8157C48487F120F90C7 FC815AA37FA26D133EA2D80FF0133C6D137CD807FE5B6D5B6CEBC3E06CEBE7C06CEBFF80 6D48C7FC6D7E010F7F013F13E0497FD801F813FC3903E03FFE3807C01F390F8007FF4848 6C1380001E1300003EEC7FC048141FED0FE0A2481407A21503A416C0127CED07807EED0F 006C141E6C6C5BD807E013F83903FC03F0C6B55A013F1380D907FCC7FC233A7DB72A>I< EB03F8EB1FFF017F7F9038FC07E03901F001F048486C7E48487F000F147C4848137E153E 003F143F48C7FC1680A248141F16C0A516E0A47E153FA27E7F001F147FA26C6C13DF1207 3903E0019F3901F8071F2600FFFE13C0EB7FFCEB1FF8EB00801400ED3F80A31600A2000F 147E487E486C5B5D14015D49485A6C48485A001EEB1F80260FC07FC7FC3807FFFC000113 F038003FC0233A7DB72A>I<121E123FEA7F80EAFFC0A4EA7F80EA3F00121EC7FCB0121E 123FEA7F80EAFFC0A4EA7F80EA3F00121E0A247AA317>I<121E123FEA7F80EAFFC0A4EA 7F80EA3F00121EC7FCB0121E123FEA7F8012FF13C0A3127F123F121F1201A4EA0380A312 071300A2120E121E121C5AA212100A347AA317>I<007FB812F8B912FCA26C17F8CCFCAE 007FB812F8B912FCA26C17F836167B9F41>61 D<1538157CA315FEA34A7EA34A7FA34A7F 153FA2020F7FEC0E1FA2021E7FEC1C0FA2023C7FEC3807A202787FEC7003A202F07FECE0 01A20101804A7EA20103814A137FA201078191C7123F91B6FC4981A2010EC7121F011E81 011C140FA2013C8101381407A201788101701403A201F08116011201486C81D80FFE0207 1380B500C090B512FEA3373C7DBB3E>65 D<B712E016FC16FF0001903980007FC06C90C7 EA1FE0707E707E707EA2707EA283A65FA216035F4C5A160FEE1FE0EE7FC04B485A91B548 C7FCA2707E91C7EA3FE0EE0FF0707E707E707E707EA21880177F18C0A7188017FFA24C13 005F16034C5AEE1FF8486DEB7FF0B812C094C7FC16F832397DB83B>I<4AB4EB0180020F EBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB079FD91FC0EB01DF4948EB 00FF49C8127F13FE4848153F4848151FA24848150F120F5B001F1607A2485AA21703127F A25B94C7FC12FFAB127FA26DED0380A2123FA36C7EEF0700120F7F0007160E6C7E5F6C7E 6C6C5D017F5D6D6C14F06D6C495AD90FF0495AD903FC010FC7FC903901FF807E6D6CB45A 020F13F002011380313D7BBA3C>I<B712C016F816FE000190398001FF806C90C7EA3FE0 EE0FF0EE03F8707E707E177FA2EF3F8018C0171F18E0170F18F0A3EF07F8A418FCAC18F8 A4EF0FF0A218E0A2171F18C0EF3F80A2EF7F0017FE4C5A4C5AEE0FF0EE3FE0486DEBFF80 B8C7FC16F816C036397DB83F>I<B812FCA30001903880001F6C90C71201707E177E173E 171EA2170EA4170F83ED01C0A394C7FCA31503A21507151F91B5FCA3EC001F15071503A2 1501A218E0A3170192C713C0A41703A3EF0780A2170FA2171F173F17FF486D010F1300B9 FCA333397DB839>I<B812F8A30001903880001F6C90C71203EE01FC1600177C173CA217 1CA4171E170EA2ED0380A21700A41507A2150F153F91B5FCA3EC003F150F1507A21503A6 92C8FCAD4813C0B612C0A32F397DB836>I<DBFF8013C0020FEBF001023F13FC9139FF80 3E03903A03FC000F87D907F0EB03CFD91FC0EB01EF4948EB007F49C8FC01FE153F484815 1FA24848150F485A000F16075B001F1603A2485AA21701127FA25B94C7FC12FFAA93B6FC 127FA26D9138007FE0EF3FC0123FA36C7EA26C7EA212076C7E6C7EA26C7E017F157F6D7E D91FE014EFD907F0EB01C7D903FCEB0783903A00FFC03F0191393FFFFE00020F01F81300 02001380383D7CBA41>I<B648B512FEA30001902680000313006C90C76C5AB3A491B6FC A391C71201B3A6486D497EB648B512FEA337397DB83E>I<B612C0A3C6EBC0006D5AB3B3 AD497EB612C0A31A397EB81E>I<017FB512C0A39039003FF800EC0FF0B3B3A3121C127F A2EAFF80A25DEB001FA2007C5C0078495A1238001E49C7FC380F81FC6CB45A000113E038 007F80223B7CB82B>I<B60107B5FCA300010180010013F06C90C8EA7F80053EC7FC5F17 705F4C5A4C5A4CC8FC160E5E5E5E5E4B5A4B5A4BC9FC150E5D153C157E15FE4A7E4A7FEC 077F91380E3FC0021C7FEC381F4A6C7E02E07FECC0074A6C7E02007F15016F7E83167F70 7E83161F707E831607831603707E83828484486D4913F0B6011FEBFF80A339397DB841> I<B612E0A3000101C0C8FC6C90C9FCB3AD1738A517781770A417F0A21601A21603160716 0FEE3FE04890388001FFB8FCA32D397DB834>I<B56C92380FFFF8A300016D92381FFC00 6C60D9EFE0153BA3D9E7F01573A3D9E3F815E3A2D9E1FCEC01C3A3D9E0FEEC0383A3027F EC0703A26E6C130EA36E6C131CA36E6C1338A26E6C1370A36E6C13E0A2913901FC01C0A3 913900FE0380A392387F0700A2ED3F8EA3ED1FDCA3ED0FF8A26F5A487E487ED80FFE6D48 497EB500E00203B512F8A2ED01C045397DB84C>I<B591380FFFFE80A2C66D010013E06E EC3F80EF1F00D9EFF0140E8013E7EBE3FC8013E1EBE0FF81147F81143F6E7E81140F6E7E 8114036E7E8180ED7F8016C0153FED1FE016F0150FED07F816FC1503ED01FE16FF81EE7F 8E17CE163FEE1FEE17FE160FA216071603A216011600A2486C157E486C153EEA0FFEB500 E0141E170EA237397DB83E>I<EC03FF021F13E091B512FC903901FE01FE903A07F8007F 80D90FE0EB1FC0D93F80EB07F049C76C7E01FE6E7E0001824914004848157F0007178049 153F000F17C049151F001F17E0A24848ED0FF0A3007F17F8491507A300FF17FCAC6C6CED 0FF8A4003F17F06D151F001F17E0A26D153F000F17C0000717806D157F6C6CEDFF000001 5E6D14016C6C4A5A6D6C495A6D6C495A6D6C495AD907F8EB7F80902703FE01FFC7FC0100 B512FC021F13E0020390C8FC363D7BBA41>I<B712C016F816FE000190398001FF806C90 C7EA3FC0EE0FE0EE07F0EE03F817FC17FE1601A217FFA717FEA2160317FC17F8EE07F0EE 0FE0EE3FC0923801FF8091B5EAFE0016F816C091C9FCB3A4487FB6FCA330397DB839>I< B612FEEDFFE016F8000190388007FE6C90C76C7EEE3FC0707E707E707EA2707EA283A65F A24C5AA24C5A4C5A4C5AEEFF80DB07FEC8FC91B512F816E0A291380007F8ED01FC6F7E16 7F707E83161F83A683A560F00380EE0FF8A3486D0107EB0700B6EB03FC933801FE0E9338 00FFFCCAEA3FF8EF07F0393B7DB83D>82 D<D90FF813C090383FFE0190B512813901F80F E33907E001F7390F80007F90C7123F48141F003E140FA2481407A200FC1403A415017EA2 7E6C91C7FC7F13E0EA3FF8EBFF806C13F86CEBFF806C14E06C14F86C806C80013F7F0107 1480D9007F13C0020713E0EC007FED1FF0150F150716F81503126012E01501A47E16F0A2 6C14036C15E0A26CEC07C06CEC0F80D8FBC0EB1F00D8F9F0133ED8F0FF13FC39E03FFFF8 010F13E0D8C00190C7FC253D7CBA2E>I<003FB812E0A3D9E003EB003F90260001FE1307 007EEE03F0007C160100781600A300701770A400F01778481738A4C71600B3B0913807FF 80011FB612E0A335397DB83C>I<B690380FFFFEA300010180010013E06C90C8EA3F80EF 1F00170EB3B27F5FA280013F5DA26D6C5C130F6E5C01074A5A6D6C13036D6C495AD900FE 011FC7FC91383F807C6EB45A020713E002001380373B7DB83E>I<B500FC91B51280A300 03018091381FF8006C90C8EA07E0606C705AA26D6C4AC7FCA280013F150EA26E141E011F 151CA26E143C010F1538A26D6C5CA28001035DA26E130101015DA26E13036D5DA26E6C48 C8FCA215C0023F130EA2EDE01E021F131CA2EDF03C020F1338A26E6C5AA215FC02035BA2 15FF6E5BA36E5BA26FC9FCA3153EA3151C393B7EB83E>I<B5D8FE01B5D8FC01B512C0A3 00039026C0000790C7381FFC006C90C76C48EC07F06C735A04015E1A016D6C6E4A5AA36D 6C4DC7FC4C7FA26E5F011F9126073FC0130EA26E171E010F020F6D131CEE0E1FA26D6C01 1E6D5BEE1C0FA26D6C5F4C6C7EA26E17F001014A6C6C5BA36D6C01F06D485AEEE001A2DA 7F804B5A923981C000FFA203C1150791263FC380D97F87C8FCA203E3158FDA1FE715CE93 C7123FA26EB415FC4B141FA202075E4B140FA36E486E5AA302015E4B1403A202005E4B14 01523B7FB855>I<007FB590387FFFFCA3C601F8010F1380D97FE0D903FCC7FC013FEC01 F06D6C5C5F6D6C13036D6C495A94C8FC6D6C5B161E6D6C131C6DEB803C5E91387FC07091 383FE0F0EDE1E091381FF1C0EC0FF3EDFB806EB4C9FCA26E5A6E7EA26E7F6F7E15FF825C 913803DFF0ED8FF8140791380F07FC91380E03FE141E91381C01FF4A7E02788002706D7E 14F049486D7E4A6D7E130349486D7E91C76C7E5B011E6E7E1601013E8101FF8200076D01 077FB500F0013FEBFF80A339397EB83E>I<B500FE91387FFFE0A3000101E091380FFE00 6C49EC07F0017F6F5A606D6C5D6D6C140795C7FC6D6C140E171E6D6C141C6D6C143C1738 6D6C14785F6D6D5B91387FC0015F91383FE0035F91381FF0076E6C48C8FC160E913807FC 1E161C913803FE3C913801FF385E6E13F05E157F6F5AB3A24B7E023FB512C0A33B397FB8 3E>I<003FB7FCA39039FC0001FE01E0130301805C90C7485A003E140F5E003C141F007C 5D00784A5A157F5E007014FF93C7FC4A5A14035DC712075D4A5A141F5D143F5D4A5A14FF 92C8FC5B5C495A13075C130F4AEB0380495A133F5C137F5C49C7FC4815075B12035B4848 EC0F00120F495C121F495C484814FF007F140349131FB8FCA329397BB833>I<EAFFF8A4 EAF000B3B3B3B3A3EAFFF8A40D5378BD17>I<48148039038001C0000713030100138000 0EEB070048130EA2485BA2485BA3485BA400EFEB778039FF807FC001C013E001E013F0A2 007F133FA2393FC01FE0391F800FC0390F0007801C1A76B92A>I<EAFFF8A4EA0078B3B3 B3B3A3EAFFF8A40D537FBD17>I<13101338137C13FE487E3803EF803807C7C0380F83E0 381F01F0383E00F848137C00F0131E0060130C170D77B92A>I<5AEA038012071300120E 5AA25AA25AA35AA412EFEAFF8013C013E0A2127FA2EA3FC0EA1F80EA0F000B1A7BB917> 96 D<EB3FE0EBFFFC000313FF3907C03F80390F800FC0486C6C7E01E07F6E7EA2380FC0 01D807807FEA0300C7FCA414FF130FEB7FF13801FF01EA07F8EA0FF0EA1FE0EA3FC0EA7F 80A2D8FF00141CA41403A2387F800714063A3FC01C7E383A1FF0787FF83A0FFFF03FF000 0301E013E03A007F000F8026277DA52A>I<EA03F812FFA3120F1203B0EC0FE0EC7FFC90 38F9FFFE9039FBE03F809039FF800FC09039FE0007E049EB03F0A249EB01F816FCA216FE 1500A216FFA916FEA3150116FCA2ED03F86D14F0ED07E06DEB0FC09039E7801F809039E3 E07F009038C1FFFE9038807FF8C7EA1FC0283B7EB92E>I<EB03FC90381FFF80017F13E0 9038FE01F03901F800F83903F001FC3807E003EA0FC0121F90388001F8003FEB00F01560 007F140090C8FCA25AA97EA27FA2003F140E7F001F141C6C7E000714386C7ED801FC13F0 3900FF03E090387FFFC0011F1300EB07F81F277DA525>I<ED1FC0EC07FFA3EC007F151F B0EB07F8EB1FFE90387FFF9F9038FE07DF3901F800FF4848137F4848133F4848131F121F 485AA2127F90C7FCA35AA97EA27F123FA2121F6C6C133F157F6C6C13FF3A03F001DFF03A 01FC079FFF39007FFF1FEB3FFED907F013C0283B7DB92E>I<EB07F8EB1FFF017F138090 38FC0FC03901F003E03903E001F0000714F8390FC000FC121F4913FE003F147EA248C712 7FA35A90B6FCA390C8FCA57EA27F123F15076C7E150E6C7E0007141C6C6C133CD801FC13 783900FF01F090383FFFC06D1380903803FC0020277EA525>I<147E903803FF80010F13 C090381FC7E090383F07F0EB7E0F13FE13FC0001EB07E09038F803C0000390C7FCADB512 FCA3D803F8C7FCB3AB487EB512F8A31C3B7FBA19>I<ED03E090390FF00FF090393FFC1F F890B5EA3C7C3A01F81FF0FC3A03E007C07C3A07C003E038000FECF000001F80EB800100 3F80A7001F5CEBC003000F5C00075C6C6C485A9038F81F800006B5C7FCEB3FFC380E0FF0 90C9FC121EA3121F6C7E90B512C015F86C14FE6CECFF8016C04815E0391F80007F48C7EA 0FF0007E140316F8481401A5007EEC03F0A26CEC07E06C6CEB0FC0D80FE0EB3F803A07FC 01FF000001B512FC6C6C13F0010790C7FC26387EA52A>I<EA03F812FFA3120F1203B0EC 07F0EC1FFCEC7FFF9138F07F809038F9C01FD9FB807F9038FF000F49805BA35BB3A4486C 497EB500E1B51280A3293A7EB92E>I<EA03C0487E487E487EA46C5A6C5A6C5AC8FCA9EA 01F812FFA312071203B3AA487EB512E0A313387EB718>I<EB01E0EB03F0EB07F8EB0FFC A4EB07F8EB03F0EB01E090C7FCA9EB01FC13FFA313071301B3B3A2123C127E00FF13F813 0314F0A2387E07E0387C0FC0383FFF00EA0FFEEA03F8164984B719>I<EA03F812FFA312 0F1203B1913803FFFCA36E13C0913800FE005D15F04A5A4A5A4A5A4AC7FC141E5C5C14FC EBF9FE13FBEBFF7F496C7EEBFC1F01F87F6E7E6E7EA26E7E6E7EA26E7E157FA2ED3F8016 C0486CEB7FF0B500E1B5FCA3283A7EB92C>I<EA03F812FFA3120F1203B3B3AD487EB512 E0A3133A7EB918>I<2703F807F8EB0FF000FFD91FFEEB3FFCDA7FFFEBFFFE913AF03F81 E07F3D0FF9C00FC3801F802603FB80D9E7007F020013E601FED907FC6D7EA2495CA2495C B3A4486C496C497EB500E1B500C3B51280A341257EA446>I<3903F807F000FFEB1FFCEC 7FFF9138F07F80390FF9C01F2603FB807F9038FF000F49805BA35BB3A4486C497EB500E1 B51280A329257EA42E>I<EB03FE90380FFF80013F13E09038FE03F83901F800FC484813 7E48487F4848EB1F80001F15C049130F003F15E0A248C7EA07F0A44815F8A96C15F0A26D 130F003F15E0A26C6CEB1FC0000F15806D133F6C6CEB7F006C6C13FE3900FE03F890387F FFF0011F13C0D903FEC7FC25277EA52A>I<3903F80FE000FFEB7FFC9038F9FFFE9039FB E07F803A0FFF801FC03A03FE000FE049EB07F0A249EB03F816FC150116FEA3ED00FFA916 FE1501A316FC150316F86DEB07F0ED0FE06D14C09039FF803F809039FBE07F009038F9FF FE9038F87FF8EC1FC091C8FCAB487EB512E0A328357EA42E>I<903903F801C090381FFE 03EB7FFF9038FE07873901FC01C73903F000EF0007147F4848133F485A003F141F5B127F A390C7FC5AA96C7EA3123F7F001F143F6C7E157F6C6C13FF3903F801DF3901FE0F9F3900 7FFF1FEB3FFCEB07F090C7FCABED3FE00207B5FCA328357DA42C>I<3803F03F00FFEB7F 809038F1FFE014C7390FF38FF03803F70F13F69038FE07E09038FC03C0EC018091C7FCA2 5BB3A3487EB512F8A31C257EA421>I<EBFF83000313E7000F13FFEA1F80383E003F487F 00787FA200F87FA37E6C90C7FC6C7EEA7FF8EBFF806C13E06C13F86C7F6C7F00017F6C7E 01031380EB003F0060EB1FC000E0130FA26C1307A37E15806C130F1500B4131EEBC07C38 F3FFF800E15B38C07F801A277DA521>I<131CA5133CA3137CA213FC120112031207121F B6FCA3D801FCC7FCB2EC01C0A93900FE0380A2017E13006D5AEB1FFE6D5AEB03F01A347F B220>I<D803F8EB0FE000FFEB03FFA3000FEB003F0003140FB3A5151FA2153F1201156F 6C6CEBEFF8903A7E03CFFF8090383FFF8F6D130FD903FCEBE00029267EA42E>I<B538C0 7FFEA33A0FFC001FF0D803F8EB07C016807F00011500A26D5B0000140EA2017F5BA2EC80 3C013F1338A26D6C5AA214E0010F5BA214F101075BA2903803FB80A214FF6D90C7FCA36D 5AA2147CA3143827257EA32C>I<B53A8FFFF07FFEA3260FF8009038800FF8000791397F 0007E0EF03C000031780816DEC80070001027F1400A26D6E5A000002FF130E15EF6DECE0 1ED97F01141C15C70281EBF03CD93F8314381583D91FC36D5AECC701A2D90FE76D5AECEE 00A2D907FEEBFFC04A137FA201035D4A133FA2010192C7FC4A7FA20100141E4A130E3725 7EA33C>I<B500C0B5FCA300039038007FF06C48EB3F806C6C013EC7FC6D133CEB3F806E 5A011F5B6D6C5A14F1903807FBC06DB45A6D90C8FCA26D5A147F818114FF497FECCFF0EB 03C790380783F890380F03FCEB0E0190381E00FE497F496D7E01F8133F000181D80FFC49 7EB548B51280A329247FA32C>I<B538C07FFEA33A07FC001FF06C48EB07C016807F0001 1500A26C6C130EA26D131E6D131CA26D6C5AA2ECC078011F1370A2ECE0F0010F5B14F090 3807F1C0A214FB01035BA26DB4C7FCA36D5AA2147CA31438A214781470A25CA21301007C 5BEAFE035C130749C8FCEAFC1EEA783CEA3FF86C5AEA0FC027357EA32C>I<003FB512FC A39038C007F8D83E0013F0003C130FEC1FE0003814C00078EB3F80147F0070EBFF005C13 01495A5CEA0007495A5C495A133F90387F800E14005B485A5B0003141E485A5B4848131C 001F143C4848137C4913FC007F1303B6FCA31F247EA325>I<B81280A3290380972A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FM cmbx10 10 48 /FM 48 122 df<913801FFC0023F13F049B512FC010780011FEB00FFEB3FF890267FE001 138049485A481380A2481300A36F13006F5A167C93C7FCA492383FFFC0B8FCA5000390C7 FCB3A9B5D8FC3F13FFA5303A7EB935>12 D<EA0F80EA1FE0EA3FF0EA7FF812FF13FCA213 FEA3127F123F121FEA0FDEEA001E133E133CA31378A213F0120113E0EA03C01207EA0F80 EA1F00120E12040F1E7AB91B>39 D<EA0780EA1FE0EA3FF0EA7FF8A2EAFFFCA4EA7FF8A2 EA3FF0EA1FE0EA07800E0E7A8D1B>46 D<49B4FC010F13E0017F13FC90B57E48EB83FF48 48C613804848EB7FC04848EB3FE049131F001F15F0A2003F15F849130FA2007F15FCA500 FF15FEB3007F15FCA4003F15F8A26D131F001F15F0A2000F15E06D133F6C6CEB7FC06C6C EBFF802601FF8313006CEBFFFE6D5B011F13F0010190C7FC27387CB630>48 D<143C14FC1301130F137FB5FCA4139FEA001FB3B3A4007FB61280A5213779B630>I<EB 0FFC90387FFFC048B512F0000714FC4880391FC03FFF263F800F1380267FC00313C06D6C 13E0EAFFF06D6C13F0A2157F16F8A26C5A6C5A6C5A6C5AC8FC16F015FF16E0A24A13C016 804A13005D4A5A4A5A4A5A4A5A5D4AC7FC14FE495AD903F013F8495A495A495A90383E00 014914F05B4848130348B6FC5A5A5A5A5AB712E0A525377BB630>I<EB03FF011F13F001 7F13FC90B57E3901FE07FF2603F0011380D807E014C0260FF80013E07F486C14F0A6000F 15E06C5A6C485AD801E014C0C714805C16004A5AEC3FF890380FFFF015C015F015FE9038 0007FF020113C06E13E0ED7FF016F8A2ED3FFCA2D80FC014FEEA3FF0487EA2487EA316FC A25B007FEC7FF85B6C48EBFFF06C484813E0260FF80713C06CB612806C1500C614FC013F 13F0010790C7FC27387CB630>I<ED0FC0151F153FA2157F15FF5C5CA25C5C5CA2143E14 7E5C495A5C495A1307495A495A5C133E137E5B485A5B1203485A485A5B48C7FC5A127E5A B81280A5C70001EBC000A90103B61280A529377DB630>I<000C15C0D81F80130701F813 7F90B6FC168016005D5D5D15E05D92C7FC14F8010EC8FC90C9FCA7EB03FE90381FFFC001 7F13F890B57E9038FC07FE9038E003FFD980011380010014C0000E6D13E0C8FC16F0A316 F8A2EA1F80487E487E487EA316F0A25B6C4814E0495A010014C06C4913806C6C48130039 0FF01FFE6CB55A6C5C6C14E06C6C1380D91FF8C7FC25387BB630>I<EC0FF8ECFFFE0103 EBFF80010F14C090391FF80FE090397FE003F09038FF800748EB000F4848EB1FF8484813 3FA2120F5B001FEC1FF0ED0FE0003FEC07C04990C7FC127FA2EC3FC0ECFFF8D8FFF113FE 01F37FD9F78113809039FF007FC049EB3FE04914F0ED1FF85B16FCA34914FEA4127FA512 3F16FCA2121F6D14F8120FED3FF06C6C14E06C6C137F3A01FF81FFC06C90B512806DEBFE 006D5B010F13F00101138027387CB630>I<123E123F13E090B71280A54816005E5E5E5E 5E007EC7EA07C0007C140F4B5A00FC4AC7FC48147E5D5D4A5AC712034A5A4A5AA24A5A4A C8FCA25C147E14FE13015C1303A31307A2495AA3131FA4133FA96D5A6D5A6D5A293A7BB8 30>I<49B47E010F13F0013F13FC497F9038FE01FF3A01F0003F804848EB1FC00007EC0F E05B000FEC07F0A2121F7FA213F87F01FFEB0FE014C09138F01FC06C13F89138FE3F806C 90B512005D6C14F86C806C806DEBFF806D14C090B612E04815F0EA07FD260FF07F13F848 486C13FC383FC00F14034848C613FE157F48C7121F15071503A21501A216FCA26C7EED03 F86C7E6DEB07F0D81FF8EB1FE0D80FFEEBFFC06CB612806C1500C614FC013F13F0010313 8027387CB630>I<EB03FF011F13E0017F13F890B57E0003EB01FF2607FC0013804848EB 7FC0153F001F15E04848EB1FF0A2007F15F8A300FF15FCA516FEA5007F143FA3123F157F 6C7E000F14FF6C6C5A3903FF03DF6CEBFF9F6CEC1FFCEB3FFEEB07F890C7FCA216F8D807 C0133F487E486C14F0487E16E0ED7FC0A249EBFF806C484813009038C007FE390FE01FFC 90B55A6C5C000114C06C91C7FCEB1FF027387CB630>I<EA0780EA1FE0EA3FF0EA7FF8A2 EAFFFCA4EA7FF8A2EA3FF0EA1FE0EA0780C7FCA9EA0780EA1FE0EA3FF0EA7FF8A2EAFFFC A4EA7FF8A2EA3FF0EA1FE0EA07800E257AA41B>I<ED03E04B7EA24B7EA34B7EA24B7EA3 4B7EA292B57EA34A8015F702038015E715E302078015C1020F801580A2021F80ED007F4A 80023E133FA2027E80027C7F02FC814A7FA20101824A7F49B77EA34982A290270FC00001 7F4A7FA2011F8291C8127F4982013E153FA2017E82017C81B500F8010FB61280A5413A7D B948>65 D<DB3FFC14C00203B5EAC003021FECF00791B6EAFC0F0103EDFE1F499039FC00 FFBF011F01C0EB1FFF4948C71207D97FF8804948804849804849157F4849153F91C9FC48 171F485A180F123F5B1807127FA25B95C7FC12FFAB127FA26DEE07C0A2123FA27F001FEF 0F80A26C7E6CEF1F00806C6D153E6C6D157E6C6D5D6D6C4A5AD93FFEEC07F090261FFFC0 EB1FE0010701FCEBFFC06D90B6C7FC01005D021F14F8020314C09126003FFEC8FC3A3B7B B945>67 D<B87E17F817FF18C018F028007FFC00077F9338007FFEEF1FFF050713807113 C0837113E019F0187F19F8183F19FC181FA219FEA419FFAC19FEA419FC183FA219F8187F 19F0F0FFE05F4D13C04D1380051F1300EF7FFE933803FFFCB912F018C095C7FC17FC1780 40397DB849>I<B912F0A528007FFC000113F8EE003F170F17071703A21701A21700A216 3E18FC187CA4047E1300A216FE150391B5FCA5ECFC031500167E181F163EA2183EA493C7 127EA2187C18FCA21701A21703EF07F8170F173FEE03FFB9FCA218F0A338397DB83F>I< B612FEA539007FFC00B3B3ABB612FEA51F397EB824>73 D<B77EA526007FFCC9FCB3AAEF 0F80A5171F1800A35FA35F5FA25E16075EEE7FFEB8FCA531397DB839>76 D<B500FC0407B512F06E5E6E5EA3C66C6D4BEBE000A2017D6D157DA2017C6D15F9A36E6C EC01F1A26E6CEC03E1A26E6CEC07C1A36E6CEC0F81A26E6CEC1F01A26E6D133EA36E6D13 7CA26E6D13F8A292397FF001F0A392393FF803E0A292391FFC07C0A292390FFE0F80A392 3907FF1F00A26F13BEA26F13FCA36F5BA2705AA2705AB500FE0303B612F0A2EE1FC0A2EE 0F8054397DB85B>I<B8FC17F017FE8318C028007FFC000713E0040113F09338007FF8EF 3FFCA218FE171FA218FFA718FEA2173F18FCA2EF7FF8933801FFF0040F13E091B7128018 0017FC17E002FCC9FCB3A2B612FEA538397DB841>80 D<B712FCEEFFE017FC17FF18C028 007FFC000F7F04017F706C7E717EA2717EA284A760173F604D5A4D5A4C5B040F5B91B7C8 FC17FC5F17FE913AFC003FFF80040F7F707F82707FA2707FAB1AE0F101F0A2EF7FFC1AE0 B600FE90383FFE0394381FFF0771EBFFC00503148005001400CBEA0FFC443A7DB848>82 D<003FB91280A5267FF801D9F00313C001E015000180163F0100161FA2007E170FA2007C 1707A400FC18E0481703A4C793C7FCB3AC011FB7FCA53B387DB742>84 D<EB3FFE0003B512E04814F84880391FF007FE393FF801FF6E7F82157F6C4880A26C5AEA 0380C8FCA291B5FC130F90B6FC0003EBF87F481380381FFC00485A5B485A485AA515FF6C 6C5A6C6C487F903AFC0FBFFFC06CB5123F0007497E6CEBF80F39007FC0032A257DA42E> 97 D<13FFB5FCA512077EAEEDFF80020F13F8023F7F91B6FCDAFE031380DAF00013C002 C0EB3FE04A14F091C7121F17F8A2EE0FFCA317FEA917FCA3EE1FF8A217F06EEB3FE06E13 7F02F0EBFFC09026FDFC07138001F8B5EAFE00023F5BD9F00F13F0D9E00190C7FC2F3A7E B935>I<903801FFC0010F13FC017F7F90B6FC48018013802607FE0113C0EA0FFC13F8EA 1FF0003F6D1380A24848EB7F00151C92C7FC12FFA9127F7FA2123F6DEB03E0121F6C6CEB 07C07F6C6CEB0F8000019038E03F006CEBFFFE6D5B010F13F00101138023257DA42A>I< EE7F80ED7FFFA5150381AEEB03FF011F13F1017F13FD48B7FC48EBC07F3907FE000F4848 7F484813015B123FA2485AA312FFA9127FA36C7EA2121F6D5B000F140FD807FE4913C06C 6C6CB512FE6CEBFFFD6C6C13F9011F13C1903803FE012F3A7DB935>I<49B47E011F13F0 017F13FC90B57E0003903881FF803907FE007F4848EB3FC04848EB1FE05B003FEC0FF0A2 485A16F8150712FF90B6FCA401E0C8FCA4127FA27F123F16F86C7E6C6C13016DEB03F06C 6CEB07E00001EBE01F6C90B51280013F1400010F13FC010013C025257DA42C>I<EC0FF8 ECFFFC010713FF491480EB3FF8D97FE113C0EBFFC114815A1401486D1380ED7F00153E92 C7FCA8B6FCA5000390C8FCB3A9B512FEA5223A7DB91D>I<163FD907FEEBFF8090267FFF E113C048B512FB489138FFDFE02607FC03131F380FF000001F159F484890387FCFC0EEC7 80007FEDE000A7003F5DA26C6C495A000F92C7FC3907FC03FE90B55A485C6D13E0261E07 FEC8FC90CAFCA2123FA213C06CB512F8EDFF8016E06C81826C816C81000F815A273FC000 0F13804848130148C8127FA56C6CECFF006C6C495AD81FF0EB07FCD80FFEEB3FF86CB65A 000115C06C6C91C7FC010713F02B377DA530>I<13FFB5FCA512077EAEED7FC0913803FF F84A7F021F7F91383F03FFDA7801138014F04A6C13C05C5CA391C7FCB3A2B5D8FC3F13FF A5303A7DB935>I<13F0EA03FC487E487EA2481380A46C1300A26C5A6C5AEA00F090C7FC A813FF127FA512077EB3A7B512F8A5153B7DBA1B>I<13FFB5FCA512077EAE92383FFFE0 A592380FF0004B5A4B5A4BC7FC15FEEC03FC4A5A4A5AEC1FC0143F4A7E4A7E81A281ECCF FEEC87FF1407496C7F6E7F6E7FA26F7E6F7E6F7EA26F7EB539F83FFFF8A52D3A7EB932> 107 D<13FFB5FCA512077EB3B3AAB512FCA5163A7DB91B>I<01FED97FE0EB0FFC00FF90 2601FFFC90383FFF8002076D90B57E021FD9FF0380DA3F03903987E07FF0DA78009039CF 001FF800074914DE6C6C48D97FFC6D7E4A5C4A5CA391C75BB3A2B5D8FC1FB50083B512F0 A54C257DA451>I<01FEEB7FC000FF903803FFF84A7F021F7F91383F03FFDA7801138000 0713F06C6C486C13C05C5CA391C7FCB3A2B5D8FC3F13FFA530257DA435>I<903801FFC0 010F13F8017F13FF90B67E0003018013E03A07FE003FF0D80FF8EB0FF8001F8149130700 3F81491303007F81A300FF1680A9007F1600A36C6C495AA2001F5D6D130F6C6C495A6C6C 495A6C6C6CB45A6C90B55A6C6C91C7FC011F13FC010113C029257DA430>I<01FFEBFF80 B5000F13F8023F7F91B6FCDAFE071380DAF00113C000079039C0007FE06C4914F091C712 3F17F8161F17FCA2160F17FEA917FC161FA217F8163F17F06EEB7FE06E13FFDAF00113C0 DAFC07138091B5EAFE00023F5B020F13F0020190C7FC91C9FCABB512FCA52F357EA435> I<49B4EB0F80011FEBE01F017F13F890B5EAFC3F00039038C07E7F48EB001F4848EB0FFF 497F48487F123F497F127FA25B12FFA9127F7FA2123F7F001F5C6D5B000F5C6CB4133F6C 01C0B5FC6CEBFFFD6C6C13F1011F13C1903803FE0190C7FCAB037F13FEA52F357DA432> I<9038FE07F000FFEB1FFC4A7E4A7E02F8138002E113C0EA07FF6C13C1A202801380A2ED 7F00151C91C8FCB3B512FEA522257EA427>I<90383FF0383903FFFEF84813FF121F383F C00FEB0003007E1301140012FEA27E6D130013F8EBFFE06C13FC14FF6C14C06C14E06C14 F0000314F8C614FC131F9038007FFE14070078130112F814007EA26C14FC6C1301018013 F89038F00FF090B512E000FD14C000F0140038E01FF81F257DA426>I<131FA55BA45BA2 5BA25A5A5A001FEBFFE0B6FCA4000390C7FCB115F8A86CEB01F014816CEBC3E090387FFF C06D13806D1300EB03FC1D357EB425>I<01FFEC3FC0B5EB3FFFA5000714016C80B3A25D A25D6C5C4B13E06CD9C03E13FF90387FFFFC6D5B6D13E00103130030257DA435>I<B539 F003FFF8A5000390C7EA3E006E137E6C157C6E13FC6C5DECE001017F5CA2ECF003013F5C ECF807011F5CECFC0F010F5C151FD907FE90C7FCA26E5A6D133E15FE6D5BA26D5BA36E5A A26E5AA26E5AA26E5A2D257EA432>I<B500F1B538807FFFA50007903B000FF80007E06C 6E6C14C0180F6C0180168082DAC00F141F6C6F14004B5CD97FE0153E17806E48147E013F 90393E7FC07C037E14FC90271FF87C3F5B17E0DAFCFC13E1010F9039F81FF1F014FD9139 FFF00FF36DEDFBE017FF6D496C5BA24B7E6D5EA26D496C90C7FCA36EC75AA2023E147C40 257EA445>I<B539F01FFFF0A500019039C007F0006C5D6D6C485A6D6C485AECF83F6D6C 48C7FC010F13FE6DB45A6D5B5D6D5B7F147F6E7E814A7E14FF497F903803FBFFD907F37F 02E17FEB0FC049486C7E013F6D7ED97F007F01FE6D7E49130FB539803FFFF8A52D257EA4 32>I<B539F003FFF8A5000390C7EA3E006E137E6C157C6E13FC6C5DECE001017F5CA2EC F003013F5CECF807011F5CECFC0F010F5C151FD907FE90C7FCA26E5A6D133E15FE6D5BA2 6D5BA36E5AA26E5AA26E5AA26E5AA2141F92C8FC5C003F133E387F807E38FFC07C14FC5C EAF80138FC07F0387E1FE0387FFFC06C90C9FC6C5AEA07F02D357EA432>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FN cmbx12 14.4 41 /FN 41 122 df<EA03F0EA0FFC487E487E48138014C0B5FC14E0A314F0A27EA27E7EEA0F FDEA03F1EA0001A2EB03E0A4EB07C0A2130F1480131F14005B137EA25B485A485AEA0FE0 121F13806CC7FC1206142977D225>39 D<153C157EEC01FE1407141F14FF13070003B5FC B6FCA3147F13F8EAFC00C7FCB3B3B3A4007FB712FEA62F4E76CD43>49 D<EC3FFC49B512E0010F14F8013F14FE90B77E4816E00007D9007F7FD80FF8010F7F01E0 6D7F484801017FD83FF06D7F01FC1680486C806D6E13C0B5FC6E6D13E0A318F082A26C90 C7FCA26C5A6C5A6C5AEA01C0C94813E0A318C05E18805E18004C5AA24B5B5F4B5B4B5B5F 4B90C7FC4B5A4B5A4B5AEDFFE05E4A5B4A90C8FCEC07FC4A48EB03F04A5A4A5A4A5A4AC7 EA07E0495A495A495A5C4948140FEB1F8049C8121F49B7FC90B812C05A5A5A5A5A5A5AA2 B91280A5344E79CD43>I<91380FFF8091B512F8010314FF010F15C0013F15F090267FF8 077F9026FF80017F4848C76C7ED803F881D807FE6E13807F486D15C06E7F486D15E0A76C 5D4A15C06C5B6C90C71480EA00FC90C8481300A24C5A5F4B5B4B5B4B5B4B5B92B5C7FC91 B512FC16F016C016FCEEFF80DA000713E0030113F89238007FFE707E70138018C07013E0 18F0A27013F818FCA3D801E016FEEA07F8EA1FFE487E487FA2B57EA218FCA44A4913F87E 91C714F06C5D01FC16E06C484A13C0494A1380D80FFE91B512002707FFE0075B000190B6 5A6C16F0013F15C0010F92C7FC010114F8D9001F90C8FC374F7ACD43>I<177E17FF5E5E A25E5E5EA25E5E93B5FC5DA25D5D5DA25DED3FBFED7F3F15FEA2EC01FCEC03F8EC07F015 E0140FEC1FC0EC3F80EC7F00A214FE495A495A5C1307495A495A495AA249C7FC13FE485A 5B1203485A485A485AA2485A48C8FC12FEBA12C0A6C96C90C7FCAE020FB712C0A63A4F7C CE43>I<0003160ED807E0153E01FCEC03FED9FFE0137F91B6FC5F5F5F5F5F5F94C7FC16 FC5E16E016804BC8FC15F0D9E07CC9FC91CAFCAAEC07FF027F13F001E1B512FC01E714FF 01EF15C09026FFF8077FDA80017F49C77F496E7E01F06E7E836C5A491680C97E18C0A218 E0A418F0A2EA07E0EA1FF8487E487EA2B5FCA318E0A34916C0007F5D4916805BD83FE016 0001805C6C6C5D6D4A5AD80FF8495B6C6C01075B2703FFC03F5B6C90B65A6C93C7FC013F 14FC010F14F0010314809026007FF8C8FC344F79CD43>I<ED0FFE92B512C0020714F002 1F14FC027F809139FFFC03FF01039038E0007F490180EB3F804990C7EAFFC04948130349 485B494815E049485B485BA2485B5AA2486F13C05C70138048923800FE0094C7FC5AA291 CAFCA25AED7FE0913801FFFE02076D7E4A14E0B548804AC67F027EEB3FFE02F86D7E4A7F 7013804A15C018E04A7F18F05C18F8A491C714FCA37EA67EA318F87E807E18F0A26C4B13 E0A26C6D15C06C7F4C13806C6D491300D97FFC495A6DB4EBFFFC6D90B55A010715E06D5D 010092C7FC023F13F8020313C0364F7ACD43>I<EA1F807F7FEBFFC091B81280A5481800 6060A260606060605A0180C86CC7FC90C912FE4C5A007E5E4C5A16074C5A4C5A484B5A94 C8FC167E16FEC8485A4B5A5E15074B5AA24B5A153FA24B5A15FFA24A90C9FCA25CA25C5D 140FA3141FA2143FA25DA2147FA314FFA65BAA6D5BA26E5A6E5AEC0F80395279D043>I< 913807FFC0027F13FC49B6FC010715C0011F15F090263FFC017F903A7FE0003FFED9FF80 130F4890C76C7E48486E1380A248486E13C0A2120F7013E0A2121F7FA27F808002F04913 C08002FE15806C6D6C5ADBE007130015F06C9138FC0FFE9238FF1FFC6CEDFFF817E06C5E 6C93C7FC7F6D15C06D15F06D810103814981011F81017F1680D9FFE715C04813C1480180 15E048EB003F4848010F14F048487F030114F848486D7E49141F007F6F13FC1603824848 80177F173FA2171FA218F8A36C7E18F0173F6C6C16E06D157F6C6CEDFFC06C6C4A13806E 5B6C01E0010F13006C01FCEB7FFE6C90B612F86C6C5D011F15C0010792C7FC010014F802 0F1380364F7ACD43>I<EA03F0EA0FFC487E487E481380A2B512C0A66C1380A26C13006C 5A6C5AEA03F0C8FCB1EA03F0EA0FFC487E487E481380A2B512C0A66C1380A26C13006C5A 6C5AEA03F0123577B425>58 D<171F4D7E4D7EA24D7EA34C7FA24C7FA34C7FA34C7FA24C 7FA34C80A24C80167E8304FE804C7E03018116F8830303814C7E03078116E083030F814C 7E031F81168083033F8293C7FC4B82157E8403FE824B800201835D840203835D02076F7F 5D844AB87EA24A83A34A8492C812014A6F80A2027E8202FE845C0101717FA24A82010385 5C0107717FA24A82010F855C496C707FB600F8021FB712E0A65B547BD366>65 D<932601FFF8EC01C0047FD9FF8013070303B600F0130F031F03FC131F92B8133F0203EF C07F020FDAF000EBF0FF4A49C7EA1FF9027F01F00203B5FC91B5008080010349C97E4949 824949824901E08249498249498290B5CA7EA24849834849187FA24849183FA25A4A181F 5AA24849180FA45A4A95C7FCA3B5FCAE7EA280A26CF20FC0A46C7FA26C1A1F6E19807EA2 6C6DF03F00A26C6D187E6C7F636D6D16016D6D4C5A6D6D4C5A6D01F8160F6D6D4C5A6D6D 4C5A01006D6CEDFF806E01F0020390C7FC021F01FEEC0FFC6ED9FFF0EBFFF8020391B612 E002005F031F93C8FC030315F8DB007F14C0040101FCC9FC525479D261>67 D<BC1280A51BC0D8000701FCC71203F0003F190F190385851A7F1A3F1A1F1BE01A0FA31A 07A318FCA21BF01A03A4050191C7FCA317031707170F177F92B6FCA69238FC007F170F17 0717031701A21B7E1700A21BFCA595C71201A21BF8A21A03A31A071BF01A0FA21A1F1A3F 1A7F1AFF070313E061193F0603B5FCBCFCA31BC0A34F517CD058>69 D<B812E0A6D8000701FCC7FCB3B3B3B0B812E0A62B527DD132>73 D<B812FCA6D8000701FCCAFCB3B3A71AFCA5F101F8A51903A31907A3F10FF0A2191F193F 197F19FF6060180F183F0503B5FCBB12E0A646527CD151>76 D<B600FE077FB512FE6F96 B6FC705FA3705FD80007F5C00070EF07DFA202F76DEF0F9FA202F36DEF1F1FA302F16D17 3EA202F06D177CA26F6C17F8A26FEF01F083A26F6DED03E0A26F6DED07C0A26F6DED0F80 A36F6DED1F00A26F6D153EA26F6D5DA2706C5DA3706D495AA2706D495AA2706D495AA370 6D495AA2706D49C7FCA2706D133EA2706D5BA3716C5BA271EB81F0A271EBC3E0A271EBE7 C0A371EBFF80A27191C8FCA2715BA3715BA2725AA2496C6F5AB76C0403B712FE725AA372 5A725A77527CD180>I<BAFC19F819FF1AC01AF01AFCD8000701F8C7001F7F0603EBFF80 060014C0073F13E07313F0851BF8851BFCA27313FEA31BFFA91BFEA34F13FCA21BF8611B F04F13E04F13C096B5128006031400061F5B92B812F8621A804FC7FC19E003FCCBFCB3AC B812E0A650527CD15C>80 D<B912F0F0FF8019F819FF1AC01AF0D8000701F8C76C7F060F 13FE06037F060080737F85737F87A2737FA387A863A34F5B6361634F5B96B5C8FC06035B 060F5B95B512F092B812C097C9FC19F86119FC9226F8000313FFDD007F7F727F727F727F 727F727FA28684A286A887A61D3C1D7E8784A2736D13FCA273EBF001B800C06D9038F803 F8739038FE07F07390B5FC070115E0736C1480080F1400CEEA7FF85F537CD164>82 D<003FBC1280A69126E0007FEBC0004848C7040F13C001F818034984498449197F49193F A290C8171FA3007E1A0FA500FE1BE0481A07A6C994C7FCB3B3AA49B912F0A653517BD05E >84 D<EC3FFF0103B512F0011F14FE017F6E7E90B712E048D9C0077F48D9800113FC486D 6C6C7E163F486D6D7E848284A2826C49816C5BA2C648C7FC90C8FCA44BB5FC4AB6FC143F 49B7FC130F013FEBF80790B512800003EBFC004813F0485B485B485B91C7FC485AA2485A A55EA26C6C5C5E6C6C147D6E01FD13F86C9026C001F9EBFFE06C9026F00FF014F06C90B5 487E0001ED803F6C6C49487E011F01F8010313E0010101C090C8FC3C387CB641>97 D<EB3FF8B5FCA61203C6FCB3A3EE7FF00303B5FC031F14E0037F14F802F9B612FE02FB90 38007FFFDAFFF8010F7F03E06D7F4B6D7F92C76C7F4A6E7F4A6F7EA2727EA285A2841A80 A41AC0AB1A80A44E1300A261A24E5AA26E4B5A804D5B03C0495B6F010F5BDAE7F0495BDA C3FED9FFFEC7FC0281B65ADA007F14F049011F14C049010749C8FC90C813E042547CD24B >I<913801FFF0021F13FF91B612E0010315F8010F81499038800FFE4948486C7ED9FFF8 491380485B4A4913C0485B5A485BA25A91C76C1380486F1300A2EE01FC484891C8FCA412 FFAB127FA27FA27EA26C6DEC07E0A27E6EEC0FC06C7FEF1F806C6D143F6C6DEC7F006C01 FE14FE6D6C495A011F9038E00FF86D90B55A01035D01001580021F01FCC7FC020113E033 387CB63C>I<943801FFC00407B5FCA6EE001F1707B3A3913801FFC0021F13F891B6FC01 0315C7010F15F749D9C01FB5FC90397FFE0003494813004801F08048498048498083485B A24890C8FCA25AA2485AA412FFAB127FA4123F7FA27EA26C7F5F6C6D5C6C6D5C6C6D91B5 FC6C6D010314F06D6C49ECFFC090393FFF803F6D90B512CF0107150F010114FCD9003F13 F00203018049C7FC42547CD24B>I<913803FF80023F13F891B512FE01036E7E010F15E0 013F01017F903A7FFC003FF8D9FFF06D7E48496D7E48496D7E5A4A6D13805A91C76C13C0 5AA24817E082485AA218F0A212FFA290B8FCA418E049CAFCA5127FA36C7EA36CEE01E0EF 03F06C7FEF07E06C7F6C6DEC0FC06C161F6C6DEC3F80D97FFCEC7F006DB4EB01FE6D9038 E00FFC010790B55A010115E06D6C1480021F49C7FC020013E034387CB63D>I<ED0FFE92 B51280020714E0021F14F0027F14F89138FFF83F499038E07FFC01071380923800FFFE5B 495A5C133FEE7FFC5C017FEC3FF8EE1FF0EE07C093C7FCADB712E0A626007FFCC8FCB3B3 A5007FB6FCA62F547CD329>I<DA1FFE14FE49B539E007FF800107DAF81F13C0011FDAFE 7F13E0017F91B612F09026FFF807143F48D9E001EBF07F48902680007F133F4804F813E0 4890C7383FFC1F19C0484891391FFE070095C7FCA2003F82A8001F5EA36C6C4A5AA26C6D 495A6C5E6C9039E001FFE06CD9F8075B4890B65A484BC8FC01E714F8D807C114E09026C0 1FFEC9FC91CBFC120FA27FA27F7F7F90B7FC17F06C16FE717E18E06C836C83846C834883 12075AD81FFCC7000114804848EC001F484815077113C0485A83A56C6C4B1380A26C6C4B 13006D5D6C6C4B5A6C6C4B5A6C01E049B45A6C01FE011F5BC690B712C0013F93C7FC010F 15FC010115E0D9000F01FCC8FC3C4F7CB543>I<EB3FF8B5FCA61203C6FCB3A3EE0FFC93 B57E030314E0030F14F84B8092393FC07FFE92387E003F4B6D7EECF9F0DAFBE0814B7F14 FF4B8192C7FCA25CA35CB3ACB6D8FC0FB612C0A642537BD24B>I<133FEBFFC0487F487F 487FA2487FA66C5BA26C5B6C5B6C5B013FC7FC90C8FCACEB1FF8B5FCA612017EB3B3A4B6 12F0A61C547BD326>I<EB1FF8B5FCA612017EB3B3B3AFB612F8A61D537BD226>108 D<D93FF8D90FFEED7FF0B591267FFFC0903803FFFE4BB500F0010F6D7E030702FC013F14 E0031F6E90B67E922A3FC07FFF01FE037F92267F001F903803F800000302FC6DD987E06D 7EC6D9F9F8ED8FC0DAFBE003DFC77F4B6D01DE143F02FF16FE4B4B8192C75CA24A5EA34A 5EB3ACB6D8FC07B6D8E03FB6FCA668367BB571>I<D93FF8EB0FFCB591B57E030314E003 0F14F84B8092393FC07FFE92387E003F00034A6D7EC6EBF9F0DAFBE0814B7F14FF4B8192 C7FCA25CA35CB3ACB6D8FC0FB612C0A642367BB54B>I<913801FFE0021F13FE91B612C0 010315F0010F15FC499038807FFE903B7FFC000FFF8049486D7F4801E001017F48496D7F A248496E7E488391C8123F4883A248834981A2007F1880A400FF18C0AC007F1880A3003F 18006D5DA26C5FA26C6D4A5AA26C6D4A5A6C5F6C6D495B6C01F801075B6D6C495B90273F FF807F90C7FC010F90B512FC6D5D010015C0023F91C8FC020113E03A387CB643>I<D93F F8EB7FF0B50103B5FC031F14E0037F14F802F9B612FE02FB01007FDAFFF8011F7F000302 E06D7FC64A6D7F92C76C7F4A6E7F4A8283727EA28584A21A80A284A21AC0AB1A8060A31A 006061A24E5AA26E4A5B6E5C6103C0495B6F011F5B6F495B9227FE01FFFEC7FC02FDB65A DAFC7F14F0031F14C0030749C8FC030013E093CAFCB0B612FCA6424D7CB54B>I<912601 FFC0EB07C0021F01F8130F91B500FE131F0103ECFF80010FEDC03F499039E01FE07F017F 90380007F04948903803F8FF4801F8EB00FD484991B5FC48824A80484980A2484980A25A 91C87E5AA35B12FFAB127FA27FA27EA2806C5EA26C6D5C6C6D5C5F6C6D91B5FC6C6D5B6C 6D5B6D6C130F903A3FFFC07FEF010F90B512CF6D150F010114FCD9003F13F00203130091 C8FCB0040FB612C0A6424D7CB547>I<90393FF003FCB5EB1FFF4B13C092B512F002F114 F89238FC7FFCECF3F000039039F7E0FFFEC65CECFF805DA25CEE7FFCEE3FF85CEE0FE093 C7FCA35CB3AAB612FEA62F367CB537>I<903901FFE007011FEBFC1F017FEBFF7F48B7FC 1207390FFE003FD81FF0130749130148487F5B007F81A200FF81A37F7F01F891C7FC13FE EBFFF06CEBFF8015FC6C14FF16C06C15F06C816C15FE6C817E6C6C1580011F15C01303D9 003F14E01400030F13F01501007C8000FC157F163F6C151FA37E17E07F7FEE3FC001F014 7F6DECFF806D4913009039FF800FFE91B55A013F5CD8FC1F14E0D8F803148027E0007FF8 C7FC2C387CB635>I<147EA614FEA41301A31303A21307A2130F131F133F137F13FF1203 000F90B6FCB8FCA5C66C48C8FCB3A8EE0FC0AB013FEC1F808017006D5C6DEB807EEDE0FE 6DEBFFFC01015C6D5C023F13C0DA03FEC7FC2A4D7ECB34>I<D91FFC913801FFC0B5020F B5FCA60003ED003FC6160FB3AD5FA35FA2017F5DA294B5FC6D6CD903F713F0DC07E7EBFF C0903A1FFF801FC76D90B512876D1507010114FC6D6C13F00207018091C7FC42377BB54B >I<B600F8010FB5FCA6C649C8EA7F801900017F167E6E15FE6D5E6F1301A26D6D5C1703 6D5E6F13076D5E6F130F6D5E6F131FA26D6D5C173F6D93C7FC6F5B027F147E6F13FE6E5C 1681A26EEBC1F816C36E5C16E76E5C16FFA26E5CA26E5CA26E91C8FCA26F5AA36F5AA26F 5AA26F5AA26F5A40367DB447>I<007FB500F890B512FEA6D8003F0180D90FF8C7FC6D6D 5C6D6D495A4D5A6D6D495A6D6D91C8FC6D6D5B6D6D485A4C5A6E6C485A6EEB8FF06EEBCF E06E13FF5F6E5C6E91C9FC6E5BA2806F7E6F7F6F7F5D4B7F8392B57E4A80EC03FDDA07F8 7F4A486C7E4B6C7F021F6D7FEC3FC04A486C7F4A486C7F49486D7F49486D7F5C01076E7F 49486E7E011F6F7FB60103B612C0A642357EB447>120 D<B600F8010FB5FCA6C649C8EA 7F00A26D6C157E18FE6D5E6F13016D5E6F1303A26D6D5C17076D6D5C170F6D5E6F131F6D 5E6F133F6D93C7FC6F5BA26E6C137E17FE6E5C16816E5C16C36E5C16E7A26EEBF7E016FF 6E5CA26E5CA26E91C8FCA36F5AA26F5AA26F5AA26F5AA35EA25E151F5E153FD81FE091C9 FC486C5B486C137E15FE487E4A5A5D14034A5A49485A007F131F9038F07FC0393FA1FF80 90B5CAFC6C13FC6C5B000313E0C690CBFC404D7DB447>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FO cmss9 9 5 /FO 5 117 df<B6FC15E015FC81EDFF80D9000113C09138007FE0ED1FF0150FED07F815 0316FC1501A4150316F81507150FED1FF0ED3FE0EC01FF90B612C016005D15F815E05D90 38001FE0140F811407816E7EA26E7E140081ED7F80A2ED3FC0A2ED1FE0ED0FF0A2ED07F8 A2ED03FCED01FEA2ED00FF283479B332>82 D<EB03FE90381FFFE0017F13F848B512FE48 805A380FFC01391FF0007E49131E4848130649130292C7FC48C9FCA57FA26C7E7FEA1FF8 EBFF806C13F86C13FF6C14C06C14F06C80013F7F010F7F01007F020F138014016E13C015 3FA2ED1FE0A2150FA60040EC1FC012700078EC3F80007E147FB46CEBFF009038F807FE90 B5FC6C5C001F14F000075CC61480D90FFCC7FC23387DB52B>I<EB0FE0EB7FFC497E0003 7F4814804814C0EBF83F391FE00FE0383FC00790388003F0EA7F001401127E00FEEB00F8 B6FCA500FCC8FC7EA2127EA2127F7F123F6D1308D81FF01378390FFC03F86CB5FC7E7E6C 14F0013F1380903807FC001D247EA222>101 D<12FEB3B3B007347BB312>108 D<EA03F8AAB512FEA53803F800B3A27F14023801FE1EEBFFFE14FF7EA2EB7FFCEB3FC018 2C7FAA1C>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FP cmr9 9 37 /FP 37 122 df<91391FE007F09139FFF81FF801079038FE7FFC903A0FE01FFC7E903A1F 803FF0FF90397E007FE0495C5B0001167E4990383F803C0003021F1300ABB812C0A33B03 F0001F8000B3A7486C497EB50083B5FCA330357FB42D>11 D<121C127E127FEAFF80A213 C0127FA2121D1201A4EA0380A3EA0700A2120EA25A5A5A12200A187AB315>39 D<EB01C01303EB0780EB0F00131E5B133813785B485AA2485AA2485AA2120F90C7FC5AA2 121E123EA3123C127CA512FCA25AAC7EA2127CA5123C123EA3121E121FA27E7F1207A26C 7EA26C7EA26C7E13781338133C7F7FEB0780EB03C01301124A79B71E>I<12C07E7E1278 7E7E120E120F6C7E6C7EA26C7EA26C7EA27F1378137CA2133C133EA3131E131FA51480A2 130FAC131FA21400A5131E133EA3133C137CA2137813F85BA2485AA2485AA2485A48C7FC 120E121E5A5A5A5A5A114A7BB71E>I<121C127E127FEAFF80A213C0127FA2121D1201A4 EA0380A3EA0700A2120EA25A5A5A12200A187A8815>44 D<B512F0A514057F921A>I<12 1C123E127FEAFF80A3EA7F00123E121C09097A8815>I<15E04A7EA34A7EA34A7EA3EC0E FEA3EC1C7FA34A6C7EA202787FEC701FA202F07FECE00FA2010180ECC007A2010380EC80 03A249486C7EA3010E6D7E010FB5FCA24980011CC77EA2496E7EA20178810170141FA201 F08149140FA20001821607487ED80FF84A7EB549B512E0A333367DB53A>65 D<B500FE90380FFFF8A3000190C7000313006C48EC01F85F17C04C5A4CC7FC160E163C5E 5E4B5A4B5A4B5A4BC8FC151E5D5D15F814014A7E4A7E140EEC1C7F4A6C7E14704A6C7E6D 486C7E02807FEC0007496D7E8215016F7E8282707E707EA2707E707E8316038383486C91 3807FF80B500FE013F13FCA336337EB23C>75 D<D8FFFE923803FFF8A3D803FF923807FE 006C5FD9DF80140EA3D9CFC0141CA3D9C7E01438A2D9C3F01470A3D9C1F814E0A3D9C0FC EB01C0A2027EEB0380A36EEB0700A391381F800EA36E6C5AA26E6C5AA36E6C5AA36E6C5A A2913800FDC0A3ED7F80A3486C6DC7FCD80FF84B7EB5D8801E90387FFFF8A33D337CB246 >77 D<B612FEEDFFC016F03A03FC0007FC0001EC00FE167FEE3F80EE1FC017E0160FA217 F0A617E0A2161F17C0EE3F80EE7F0016FEED07FC90B612F016C04BC7FC01FCC9FCB3487E B512F8A32C337DB234>80 D<007FB712FEA39039C007F001D87E00EC007E007C163E0078 161E170E127000F0160FA3481607A6C71500B3AB4A7E011FB512FCA330337DB237>84 D<B5D8F007B590381FFFF0A3D803FEC7D83FF0010313006C48DA1FC0EB00FC1A786D6E7E 00001970A27114F0017F60A24C7E6D6C4C5AA24C7E6D6C01394A5AA2EE79FE6D6C01704A C7FCA2EEF0FF6D6C496C130EA21501D903F8496C6C5AA3913BFC03801FC03C01011738A2 913BFE07000FE07801001770A2DAFF0E903807F0F0027F5EA24BEB03F9DA3F9C5DA203B8 EB01FDDA1FF8ECFF80A36E486D90C8FCA36E48147EA36E48143CA34C357FB24F>87 D<EB7F803803FFF04813FC380F80FE381F003F486C6C7E6D6C7EA26E7EEA1F80EA0F00C7 FCA3EB03FF133F3801FFC73803FC07EA0FE0EA1FC0EA3F80EA7F00A200FEECE1C0A4140F A2007F131B393F8033F33A1FC0E1FF80260FFFC113006CEB80FE3900FE007C22237DA126 >97 D<EA03F012FFA312071203AEEC3FC0ECFFF001F313FC9038F7C0FE9038FE003F49EB 1F8049EB0FC05BED07E0A216F01503A216F8A816F0A2150716E0A26DEB0FC016806DEB1F 0001EE133E9038C781FC9038C3FFF8018113E0C7EA3F8025357EB32B>I<EB07F8EB3FFF 90B512803901FC07C03903F003E03907E007F0380FC00FEA1F80A2393F0007E0EC03C048 90C7FC127EA212FEA8127E127FA26C14387F001F14706C7E6C6C13E03903F001C03901FE 07806CB51200EB3FFEEB07F01D237EA122>I<153FEC0FFFA3EC007F81AEEB0FF0EB7FFC 90B5FC3901FC0FBF3907E001FF48487E497F001F8048C7FCA25A127EA212FEA8127EA212 7F7EA26C6C5B5D6C6C5A6C6C4813803A03F81F3FFC3801FFFE38007FF8D91FE013002635 7DB32B>I<EB0FE0EB7FFC497E3801F83F3903E00F803907C007C0390F8003E0121FD83F 0013F014015A007E14F8A212FEB6FCA348C8FCA5127E127FA26C14386C7E15706C7E6C6C 13E03903F001C03901FE07806CB51200EB3FFEEB07F01D237EA122>I<14FEEB03FF010F 138090381F8FC090383E1FE0137C13F81201EC0FC03903F0078091C7FCABB512F0A3D803 F0C7FCB3A7487E387FFFE0A31B357FB417>I<151F90391FC07F8090387FF0FF3A01FFFD E7C03903F07F873907C01F073A0F800F8380001FECC000EB00074880A76C5CEB800F000F 5C6C6C48C7FCEBF07EEBFFFC380C7FF0EB1FC0001CC9FCA2121EA27EEBFFFE6CEBFFC015 F06C80000F80391F0001FE003EEB007F48141F168048140FA5007CEC1F00A2003F147E6C 6C5B390FF007F80003B512E0C61480D91FFCC7FC22337EA126>I<EA03F012FFA3120712 03AEEC1FC0EC7FF09038F1FFF89038F3C0FC9038F7007E13FE497F5BA35BB3486CEB7F80 B538C7FFFCA326347EB32B>I<1207EA0F80EA1FC0EA3FE0A3EA1FC0EA0F80EA0700C7FC A9EA07E012FFA3120F1207B3A6EA0FF0B5FCA310337EB215>I<EA03F012FFA312071203 AF913807FFE0A36E1300EC01F8EC03E05D4A5A020EC7FC143C5C5C13F1EBF3F813F7EBFE FCEBFC7EEBF83E497E816E7E1407816E7E1401816E7E81486C7FB500C313F0A324347EB3 29>107 D<EA07E012FFA3120F1207B3B3A7EA0FF0B5FCA310347EB315>I<2703F01FE013 FF00FF90267FF80313C04A6C487F903BF3C0FE1E07F03C07F7003F3801F8D803F6143001 FC90391FE000FC495CA3495CB3486C496C487EB53BC7FFFE3FFFF0A33C217EA041>I<39 03F01FC000FFEB7FF09038F1FFF89038F3C0FC3907F7007EEA03FE497F5BA35BB3486CEB 7F80B538C7FFFCA326217EA02B>I<EB07F0EB3FFE90B57E3901F80FC03903E003E04848 6C7E48486C7E001F8090C7127C48147E003E143E007E143FA300FE1580A8007E1500A200 7F5C6C147EA26C6C5BA26C6C485A6C6C485A3903F80FE0C6B51280D93FFEC7FCEB07F021 237EA126>I<3903F03FC000FFEBFFF001F313FC9038F7C0FE3907FE007F6C48EB3F8049 EB1FC049130F16E0150716F0A2150316F8A816F01507A216E0150F6D14C0ED1F806DEB3F 006D137E9038F781FC9038F3FFF801F113E09038F03F8091C8FCAA487EB512C0A325307E A02B>I<90380FE00790383FFC0FEBFFFE3801FC0F3903F0039F3907E001DF48486CB4FC 48487F123F90C77E5AA2127E12FEA8127E127FA27E6D5B121F6D5B6C6C5A3907F007BF39 03F81F3F3800FFFEEB7FF8EB0FE090C7FCAAED7F8091380FFFFCA326307DA029>I<3803 E07C00FF13FF01E113809038E39FC03807E71FEA03EE9038EC0F809038FC070049C7FCA3 5BB2487EB512E0A31A217FA01E>I<EBFF06000713CE4813FEEA1F00003C133E007C131E 127800F8130EA37E6C90C7FCEA7F8013F86CB47E6C13E06C13F86C7F00017F38000FFF13 00EC3F800060131F12E0140F7EA27E15006C5B6C133E38FF80FC38F7FFF800E113E038C0 7F8019237EA11E>I<1370A513F0A31201A212031207120F121FB512FEA33803F000AF14 07A8140EEA01F8A23800FC1CEB7FF8EB3FF0EB0FC0182F7FAD1E>I<D803F0133F00FFEB 0FFFA30007EB007F000380B3A25DA25D12019039F801BF803A00FC073FFCEB7FFEEB3FFC D907F0130026227EA02B>I<B53801FFF0A33A0FF0007F806C48EB1F006D131E0003141C 153C6C6C1338A26D137800001470A2017E5BA2EB7F01013F5BA290381F8380A214C7010F 90C7FCA2EB07EEA214FE6D5AA26D5AA36D5AA224217E9F29>I<B53A1FFFC3FFF0A33C07 F800FE007F804949EB3E000003161CA26D486C133C00011638A26D486C13780000029F13 70A2D9FE07EB80F0017E010F5BA2D97F0F13C190263F0E075BA2029E13E390261F9C035B A202FC13F790260FF80190C7FCA216FF6D486C5AA36D48137CA36D48133834217F9F37> I<B53803FFF8A32603FC0013800001ECFC0000005C017E5B90387F01E090383F83C0011F 5BEB0FC7D907EFC7FC14FE6D5A6D5A6D7E80497E5BECDF809038079FC090380F0FE0EB1E 0790381C03F090383C01F801787FEBF0000001147ED80FF813FF26FFFC0313FCA326207F 9F29>I<3A7FFF80FFF8A33A07F8003FC06C48EB1F806C6CEB0F00150E6D131E0000141C A2017E5BA2017F13786D1370A26D6C5AA214C1010F5B14E301075BA2D903F7C7FCA214FF 6D5AA26D5AA31478A21470A214F05CA2495A127CEAFE035C49C8FC5BEAFC1EEA783CEA3F F86C5AEA07C025307F9F29>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FQ cmbx9 9 7 /FQ 7 117 df<ED1F80A24B7EA24B7EA34B7EA24A7FA34A7FA24A7F15DFA2020F7F158F 021F801507023F80143E81027E80EC7C0102FC804A7EA20101814A137F0103814A133FA2 01078191B6FC4981A2498291C7120F824982013E80017E82137C8201FC824980B500F001 7FEBFFF0A43C347DB343>65 D<EB7FFE0003B512E04814F84880391FF80FFEEC03FF6E13 808016C06C5A6C5AEA0180C8FC91B5FC131F48B6FC000713F8481300EA1FFCEA3FF0485A 485AA56C6C5A5C263FF81F13E06CB5EA7FFF6C497E0003EBF81F39007FC00728217EA02B >97 D<13FE12FFA4120F1207ADEC07FE91383FFFC090B612F0829138F00FFC9138C003FE 91380001FF491580A26F13C0A317E0A917C0A34B138017006D5B9138C007FE9138F01FFC 01FBB55A01F014E0D9E03F13809026C007FCC7FC2B347EB331>I<903807FF80013F13F0 90B512FC48800007EB03FFEA0FFCEA1FF813F0123F6E5A48486C5A153000FF91C7FCA912 7F7F123FED0F806C7E6DEB1F006C6C5B3907FF80FE0001EBFFFC6C14F0013F5B010790C7 FC21217DA027>I<3901FC1F8000FFEB7FF0ECFFF801FD13FCECE7FE380FFFC76C1387A2 1407EC03FCEC01F89038FE00601500B1B512F8A41F217EA024>114 D<9038FFE1C0000313FF120F5A383F803F387F000F007E130712FEA26C90C7FC13E013FF 14F06C13FC6C13FF15806C14C012076C14E0C66C13F01303EB001F0078130F00F813077E 15E07E6C130F9038C03FC090B51280150000F913FC38E03FE01C217DA023>I<133EA513 7EA313FEA2120112031207121FB61280A4D807FEC7FCB0EC07C0A70003EB0F8013FF6CEB FF006C5B6D5AEB0FF01A2F7EAE22>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FR cmsy8 8 7 /FR 7 123 df<14C0497E497E497EEB0F3CEB1E1E497E496C7E496C7E48486C7E48486C 7E4848137848C77E001E80488048EC0780481403007814076CEC0F006C141E6C5C6C6C5B 6C6C5B6C6C485A6C6C485A90387807806D48C7FCEB1E1E6D5AEB07F86D5A6D5A6D5A2121 7FA024>5 D<027FB512C00107B6FC131FD93F80C8FC01F8C9FC485AEA03C0485A48CAFC 120E5AA25AA25AA35AA91270A37EA27EA27E120F6C7E6C7EEA01F0EA00FCEB3F806DB612 C01303EB007F91C9FCAD003FB712C05A7E2A3B7AAB37>18 D<17C01603160FEE3F0016FC ED03F0ED0FC0033FC7FC15FCEC03F0EC0FC0023FC8FC14FCEB03F0EB0FC0013FC9FC13FC EA03F0EA0FC0003FCAFC12FC12F012FC123FEA0FC0EA03F0EA00FC133FEB0FC0EB03F0EB 00FC143FEC0FC0EC03F0EC00FC153FED0FC0ED03F0ED00FC163FEE0F80EE03C0160193C7 FCAD007FB71280B812C0A22A3B7AAB37>20 D<1604160E82A2707EA2707E707E1770A283 B812FC17FF6C83CAEA03C0EF00F0187C181FF00FE0F003FC1801F007E0F01F80F03E0018 F8EF01E04D5A007FB8C7FCB85A5FCA12385F5FA24C5A4C5AA24CC8FCA2160E16043E297C A447>41 D<387FFFC0B512F86C13FEC7123FEC07C06E7EEC00F0157881151C81A281A2ED 0380A3ED01C0A3B7FCA3C81201A3ED0380A3ED0700A2150EA25D153C5D5DEC03E04A5A02 3FC7FC387FFFFEB512F86C13C0222B7AA52F>51 D<1330137813FCA61378A51330A2003C 13F0387F33F8B512FCA2387F33F8383C30F0000013001378A413FCB3A41378AC1330163D 7CAE1F>121 D<1330137813FCA51378A41330003C13F0387F33F8B512FCA2387F33F838 3C30F0000013001378A413FCA51378133090C7FC1330137813FCA51378A41330003C13F0 387F33F8B512FCA2387F33F8383C30F0000013001378A413FCA513781330163D7CAE1F> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FS cmr12 12 53 /FS 53 123 df<EA01FC12FFA4120712031201B3AE487EB512F8A4152C7DAB1C>16 D<131F1480133F137F13FF1400485A485A485A5B485A485A5B003EC7FC5A5A5A12601112 6CC431>19 D<0060EB01800078130700FCEB0FC0003FEB3F00381F807E380FE1FC3803F3 F06CB45A6C5B6D5A011EC7FC130C1A0C75BF31>I<13FEA3EBFFC014F0EB0FF8EB03FC13 01EB00FEA41301EB03FCEB0FF8387FFFF0B512E0EBFE000080C7FC1713747D2B>24 D<140E141E143C147814F0EB01E0EB03C0EB0780A2EB0F00131E133E133C137C137813F8 5B12015B1203A2485AA2120F5BA2121F90C7FCA35AA2123EA2127EA5127CA212FCB2127C A2127EA5123EA2123FA27EA37F120FA27F1207A26C7EA212017F12007F1378137C133C13 3E131E7FEB0780A2EB03C0EB01E0EB00F01478143C141E140E176477CA26>40 D<12C07E7E12787E7E7E6C7EA26C7E6C7E7F12007F1378137C133C133E131E131FA2EB0F 80A214C01307A214E01303A314F0A21301A214F8A51300A214FCB214F8A21301A514F0A2 1303A214E0A3130714C0A2130F1480A2EB1F00A2131E133E133C137C137813F85B12015B 485A485AA248C7FC121E5A5A5A5A5A16647ACA26>I<121E123FEA7F80EAFFC0A313E012 7F123F121E1200A5EA01C0A4EA0380A2EA0700A2120E121E121C5A5A12200B1D78891B> 44 D<14FF010713E0011F13F890383F81FC9038FE007FD801F8EB1F8049130F000315C0 4848EB07E0491303000F15F0A24848EB01F8A2003F15FCA390C8FC4815FEA54815FFB3A4 6C15FEA46D1301A2003F15FCA3001F15F8A26C6CEB03F0A26D1307000715E06C6CEB0FC0 6D131F6C6CEB3F806C6CEB7F0090383F81FC6DB45A010713E0010090C7FC28447CC131> 48 D<1438147814F81303130F137FB5FCA213F71387EA0007B3B3AFEB1FFE007FB61280 A4214278C131>I<EB03FE90381FFFC0017F13F090B57E3903F00FFE3907C003FF48C713 80000EEC7FC048EC3FE0003C141F003815F048140F16F8127CB414076D14FC7FA46C5AA2 6CC7FCC8FC16F8150FA216F0151F16E0ED3FC0A2ED7F80160015FEA24A5A4A5A4A5A5D4A 5A4AC7FC143E5C5C495A5C495A4948131C49C7FC131E4914385B5B485A491478485A48C8 12F048B6FC5A5A5AB7FC16E0A326427BC131>I<ED0780150FA2151FA2153F157FA215FF 5CA25C5C157F140F140E141C143C1438147814F014E01301EB03C014801307EB0F00130E 131E131C5B1378137013F0485A5B1203485A90C7FC5A120E5A123C123812785AB812C0A4 C8387F8000AC4B7E91B612C0A42A437DC231>52 D<14FF010713E0011F13F84913FE49C6 7E01F8EB3F804848EB0FC0D803C0EB07E00007140349EB01F0120F90C7FCED00F85AA37F A27FED01F07FD80FF8EB03E07F6CB4EB07C09138800F806C9038E01F006CEBF03EECFC7C 6CEBFFF06D5B011F5B6D13F001037F010F13FE90383F7FFFD97C3F1380D9F80F13C02601 E00713E02603C00113F048486C13F8000FEC3FFC48C7121F003EEC07FE1503481400167F A248153FA2161FA4161E7E127C163C7E003F15786C15F06C6C1301D807E0EB03E0D803F8 EB0FC06CB4EBFF806C9038FFFE00013F5B010F13F0010190C7FC28447CC131>56 D<121E123FEA7F80EAFFC0A4EA7F80EA3F00121EC7FCB3A5121E123FEA7F80EAFFC0A4EA 7F80EA3F00121E0A2B78AA1B>58 D<ED01E0A34B7EA34B7EA34B7EA24B7EA34B7E1539A2 03797F1570A203F07FEDE07FA2020180EDC03FA2020380ED801FA2020780ED000FA24A80 020E1307A24A801603A24A8082A24A8182A24A8191B7FCA24982A202C0C7123F49486E7E A349C86C7EA24982010E1507A2011E82011C1503A2013C820138811378017C83EA01FE26 07FF8002077FB500F091B612C0A442477DC649>65 D<B8FC17E017FC17FFC69026E00003 7F6D4801007FEF3FE0717E717E84170784170384A860170760170F604D5A4D5AEFFFC04C 5BDC0FFEC7FC91B612F817E017FE913AC00001FF809338007FE0EF1FF0717E717E717E71 7E19808319C0187FA219E0A719C018FFA24D1380A24D13005F4D5A4D5AEF7FF8496C4948 5AB912C095C7FC17FC17C03B447CC345>I<DB0FFC146092B500C013E0020314F0020FEC FC01913A3FFE00FE03DAFFE0131F490180EB07874948C7EA03CFD90FF8EC00EF4948157F 4948153F495A4A151F49C9120F485A000317075B00071703485AA248481601A3485A1800 A2127FA2491700A212FFAC127FA27F19E0123FA36C7EA2F001C06C7EA26C6C1603000318 807F0001EF07006C7E6D6C150E6E151E6D6C5D6D6C15386D6C15F0D903FE4A5A6D6C6CEB 07C06D01E0EB1F80DA3FFE01FFC7FC020FB512FC020314F0020014C0DB0FFEC8FC3B487B C546>I<B8FC17F017FC17FFC69026E0000713C06D4801007FEF1FF0EF0FFCEF03FE717E 83727E727E727EA2727E85180785A2180385A3727EA41A80AD1A00A44E5AA36118076118 0F61181F614E5A187F4E5A4D90C7FC4D5A4D5AEF1FF8EF7FE0496C903807FFC0B9C8FC17 FC17F094C9FC41447CC34B>I<B912FCA4C601E0C7EA3FFE6D4814071701EF007EA2183E 181EA284A384A40407EB0380A495C7FCA35EA25E5E16FF91B6FCA4ECC000163F8282A282 19E0A3F001C0A393C7FCA318031980A21807A3180FA2F01F0060604D5A1707496C147FBA FC60A33B447DC342>I<B912F0A4C601E0C713F86D48141F170717011700A21878A2183C A3181CA4180E160EA31800A4161EA2163E167EED01FE91B5FCA4ECC001ED007E163E161E A2160EA793C8FCAFEBFFF0B612FCA437447CC340>I<B612F8A439007FF0006D5AB3B3B3 A4497EB612F8A41D447DC323>73 D<010FB6FCA4D9000313C002001380B3B3AA120EEA3F 80487E487EA316005C13C0D87F805BEB000300385C003C495A6C5C390F801FE03907E03F C00001B5C7FC6C13FCEB1FE028467CC332>I<B600E00107B512C0A4C601E0C8EBF8006D 48ED7F80067EC7FC187C1870604D5A4D5A4DC8FC170E5F5F5F5F4C5A4C5A4CC9FC160E5E 5E5E5E150115034B7E4B7E151F4B7EED77FE15E39138C1C3FFDAC3817FECC70002CE8002 DC6D7E02F8133F4A804A131F4A6D7E831607707E8382707F84177F84717E171F84717E17 07841703717E858585496C4A13F8B600E0013FEBFFE0A443447CC34C>I<B612FCA4C601 F0C9FCEB7FC0B3B21870A518E0A51701A3170318C01707A2170F171F173F17FF1603496C 131FB91280A434447CC33D>I<B500E00407B5FCA36E5EC61A00D977F8EE1DFEA3D973FC 1639A3D971FE1671A2D970FF16E1A36E6CEC01C1A36E6CEC0381A26E6CEC0701A36E6C14 0EA36E6C141CA26E6C1438A36E6C1470A36E6C14E0A292397F8001C0A392393FC00380A3 92391FE00700A292380FF00EA36F6C5AA36F6C5AA26F6C5AA36F6C5AA3705AA201F86E5A 487ED807FF4D7EB500F890261F0003B6FCA3160E50447CC359>I<B712FEEEFFE017F817 FEC6903AE00007FF806D4801007FEF3FE0717E717E717E717EA28483A21980A81900A25F 606017074D5A4D5A4D5AEFFFC0040790C7FC91B65A17F017C002C0CAFCB3A8497EB612E0 A439447DC342>80 D<B712E016FF17C017F8C69039E0003FFC6D48EB03FF04007F717E71 7E717E717EA284170784A760A2170F604D5AA24D5A4D5A4C48C8FCEE07FEEE3FF891B612 E094C9FCA29139C0007FC0EE1FF0EE07F8707E707E838284177F84A784A71AE084173FA2 051FEB01C0496C15F8B600E0130F943907FC0380943903FE0F00943800FFFECBEA3FFCF0 07F843467CC348>82 D<49B41303010FEBE007013F13F890B56C5A3901FE00FFD803F8EB 1F9FD807E0EB07FF48487F48487F8148C87E825A007E81A212FE82A46C81A36C7E6D91C7 FC7F7FEA3FFC6CB47E14F86CEBFF806C14F86C14FE6C6E7E6C15E06D80011F80010780D9 007F7F14079138007FFF030F138015031500EE7FC0A2163FEE1FE0126012E0160FA47EA2 17C07E161F6C1680A26CED3F007E6D147E6D5CD8FDF01301D8F8FE495A3AF07FC01FF06D B512C0D8E00F5C010149C7FC39C0003FF02B487BC536>I<003FB912F8A4903BF8003FF8 003F01C06D48130748C7ED01FC007E1700007C187C0078183CA30070181CA500F0181E48 180EA5C81600B3B3A4ED7FFC0103B77EA43F447DC346>I<B600E0011FB5FCA4C601E0C8 13E06D48ED3F80F01F00180EB3B3A7013F161E181C80A2011F5EA26D6C157818706D6C15 F001035E6E4A5A01014B5A6DB4140F6E6C49C7FCDA3FE0137E91390FFC03FC6EB512F002 015C6E6C1380DB07FCC8FC40467CC349>I<B66C91387FFFF0A4000101F0C8000F13006C 01C0ED03F8017F705A6E5E013F5FA280011F4C5AA26E1507010F94C7FC800107160EA280 01035EA26E153C6D1638A26F14786D167081027F5DA26F1301023F5DA26F1303021F5D81 020F4AC8FCA26F5B0207140EA26F131E0203141C816E5CA216806E5CA2EEC0F0037F5B16 E092383FE1C0A216F192381FF380A216FF6F90C9FCA36F5AA26F5AA36F5AA36F5AA24446 7EC349>I<EB0FFC90B57E48803903F00FF03907C003F8486CC67E001F147E6D137F8182 6C5A6C486D7E6C5AC8FCA6EC1FFF49B5FC90380FFE1FEB7FE03801FF00EA03FCEA07F048 5A485A123F485AA290C714E05AA3153FA36C6C136F15EF3B3FC001C7E1C0391FE003873B 0FF81F07FF802703FFFE0313006C9038F801FE3A001FE000FC2B2E7CAC31>97 D<EA01FC12FFA4120712031201B2EC01FE91380FFFC0023F13F091387C03F89138F000FE D9FDC0137FD9FF80EB1F8091C713C049140F49EC07E017F0160317F8A217FC1601A317FE A917FCA21603A217F8A2EE07F0A26DEC0FE017C06DEC1F80D9FB80EB3F00D9F1C0137E90 39F0E001FC9039E07C07F891383FFFE0D9C00F1380C7D803FCC7FC2F467DC436>I<EC7F C0903803FFFC010F7F90383F803F90397E000F8049EB1FC0484814E04848133F485A120F 49EB1FC0001FEC0F804848EB070092C7FCA2127FA290C9FC5AAA7EA27FA2123F6D147012 1FA26C6C14E06C7E0003EC01C06C6CEB03806C6C1307017FEB0F0090383FC07E90381FFF F8010713E001001380242E7DAC2B>I<167FED3FFFA415018182B2EC7F80903803FFF001 0F13F890383FC07E90387F000F01FC6D5A48481301485A48487F000F81485AA2485AA212 7FA290C8FCA25AA97EA37F123FA2121F7F000F5D6C6C5B7F00034A1380D801FC9038077F C06C6C011E13FE90383F80FC90381FFFF0010713E00100010013002F467DC436>I<EB01 FE903807FFC0011F13F090387F03F89038FC00FC4848137E48487F4848EB1F80A24848EB 0FC0121F4914E0003F1407A2127F90C713F0A35A90B6FCA390C9FCA67EA27F123FA21670 6C7EA26C6C14E012076C6CEB01C06C6CEB03806C6CEB0700017F130E90383FC07C90380F FFF8010313E0010090C7FC242E7DAC2B>I<EC0FE0EC3FF8ECFFFE903803F83F903807E0 7F90390FC0FF80495AA2495A49EB7F00153E017E131C01FE90C7FCAFB67EA4C648C8FCB3 B0487E007F13FFA421467EC51E>I<EE1F80D901FCEB7FC0903A0FFF81FFE0013F9038E3 E1F090397E03F7039038F800FE484890387C01E0000391387E00C048486D1300A248486D 7EA2001F81A7000F5DA26C6C49C7FCA26C6C137E0001147C6C6C5B3901FE03F039033FFF E0010F1380260701FCC8FC0006CAFCA2120FA46C7E13E090B512F86CECFF806C15E06C81 16FC0003813907E0000FD80F80EB01FF48C8EA7F80003E153F007E151F007C16C000FC15 0FA5007C1680007E151F6CED3F00A26C6C147ED80FE0495AD803F8EB07F06CB4EB3FE06C 6CB51280011F49C7FC010113E02C427DAC31>I<EA01FC12FFA4120712031201B2EC01FE 913807FFC04A13F091383E07F8EC70014A6C7E4A7FEBFD8001FFC7127E167F5BA35BB3A8 486CECFF80B5D8F83F13FEA42F457DC436>I<EA01E0487E487E487EA46C5A6C5A6C5AC8 FCADEA01FC12FFA4120712031201B3AE487EB512F8A415437DC21C>I<EA01FC12FFA412 0712031201B392387FFFE0A492381FFE00ED0FF016C093C7FC151E5D5D5D4A5A4A5A4A5A 4AC8FC5C4A7E147F4A7E9038FDCFE0EBFF87EC07F0496C7EEBFC01816E7E157E157F6F7E 151F826F7E1507826F7E8282486C497EB5D8F81F13F8A42D457DC433>107 D<EA01FC12FFA4120712031201B3B3B3A3487EB512F8A415457DC41C>I<D801FC01FFEC 1FE000FF010701E0EBFFFC4A6D487F913B1E03F803C07F913C3800FC07001F8000070160 D9FE0C80000349D97F186D7E2601FD805C01FFDA3F70130791C74980495DA3495DB3A848 6C4A6C497EB5D8F81FB50003B512E0A44B2C7DAB52>I<3901FC01FE00FF903807FFC04A 13F091383E07F8EC70010007496C7E0003497F3801FD8001FFC7127E167F5BA35BB3A848 6CECFF80B5D8F83F13FEA42F2C7DAB36>I<EC7F80903803FFF0010F13FC90383FC0FF90 397E001F80496D7ED801F0EB03E000038148486D7E48486D7EA24848147E003F157FA348 C8EA3F80A44816C0AA6C1680A26D147F003F1600A2001F157E6D14FE000F5D6D13016C6C 495A6C6C495A6C6C495A6C6C495A90263FC0FFC7FC6DB45A010713F89038007F802A2E7D AC31>I<3901FC01FE00FF90380FFFC0023F13F091387C07F89138F001FE3A07FDC0007F 6CB448EB3F806C90C7EA1FC05B49EC0FE017F0160717F8160317FCA3160117FEA917FC16 03A317F8160717F0160F6D15E0EE1FC06DEC3F806EEB7F00D9FDC013FE9039FCE001FC91 387C0FF891383FFFE0020F1380DA03FCC7FC91C9FCAD487EB512F8A42F3F7DAB36>I<39 03F807E000FFEB1FF8EC3FFCEC78FEECE1FF3807F9C100031381EA01FBEC00FE01FF137C 4913381500A35BB3A7487EB512FEA4202C7DAB26>114 D<90383FE0183901FFFC3848EB FF78390FE01FF8381F0003003E1301003C1300481478A212F81538A37E7E6C1400EA7FC0 13FC383FFFE06C13FC6C13FF6C14806C14C0C614E0011F13F0010013F8EC0FFC14030060 130000E014FE157E7E153EA37E153C7E157C6C14786C14F039FB8003E039F1F00FC000F0 B5128039E07FFE0038C00FF01F2E7DAC26>I<130EA6131EA4133EA2137EA213FE120112 031207001FB512F0B6FCA3C648C7FCB3A3151CAA017E1338137FA26D1370EB1F8090380F E1E0903807FFC06D13809038007E001E3E7EBC26>I<D801FC147F00FFEC3FFFA4000714 01000380000181B3A75EA35D12005D6DEC7F80017E010613C06D011C13FE90381FC07890 380FFFF06D13E00100018013002F2D7DAB36>I<B539F003FFFCA4000390C7EA7FE0D801 FCEC3F006D141E0000151CA26D143C6D1438A26D6C5BA26E13F0011F5CA2ECE001010F5C A26D6C485AA2ECF807010391C7FCA26E5A0101130EA26D6C5AA2ECFF3CEC7F38A215F86E 5AA26E5AA36E5AA36E5AA22E2C7EAA33>I<B539F007FFFCA40001D9C00313C03B007F80 01FE00013FEB00F86E485AD91FE05B010F495AD907F05BECF8076D6C48C7FC0101131EEC FE1C903800FF3C6E5A6E5A5D141F140F6E7E81140F4A7EEC3DFEEC38FFEC787F4A6C7ED9 01E07FECC01F01036D7ED907807F49486C7E010E1303011E6D7E013E8001FE6D7ED807FF 01031380B5D8C00F13FFA4302B7FAA33>120 D<B539F003FFFCA4000390C7EA7FE06C48 EC3F00163E0000151CA2017F5CA280013F5CA26E13F0011F5CA26D6C485AA2ECF0030107 5CA26D6C48C7FCA214FC0101130EA2ECFE1E0100131CA2EC7F38A215F86E5AA26E5AA36E 5AA36E5AA292C8FCA25C140EA25CA3003C5B127EB45BA25C130148485A387C0780011FC9 FCEA3FFEEA0FFCEA03F02E3F7EAA33>I<003FB612E0A39039E0003FC001801480003EC7 127F003CECFF005D0038495A007813034A5A5D0070130F4A5A5D143F4A5AC748C7FC5C13 01495A5C1307495A4A13E0131F495A495AEC00014914C0485A5B1203484813035B484813 07121F4848130F49EB3F80007FEB01FFB7FCA3232B7DAA2B>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FT cmsy10 12 3 /FT 3 34 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<147014F8A8003815E000 7CEC01F000FEEC03F8D8FF80130FD87FC0EB1FF001E0133F3A1FF870FFC02607FC711300 3901FF77FC39007FFFF0011F13C0010790C7FCEB01FCEB07FF011F13C0017F13F03901FF 77FC3907FC71FF261FF87013C03A7FE0F83FF001C0131FD8FF80EB0FF8D8FE001303007C EC01F00038EC00E0C71400A81470252B7AAD32>3 D<1A601AF0A2861A78A386A286A286 A2747E871A03747E747E1B781B7C1B3FF30F80F307E0757E007FBC12FEBE1280A26CF3FE 00CEEA03F0515AF30F80093FC7FC1B7C1B7863505A505A1A076350C8FCA21A1EA262A262 A31AF862A21A6059347BB264>33 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FU cmr17 17.28 15 /FU 15 117 df<B712E0A4C60280CAFCD93FFCCBFC131F5CB3B3B21A1CA61A3C1A38A61A 78A41AF8A21AF01901A219031907A2190F191F193F197FF001FF1807013F043F13E0D9FF FC0203B5FCBBFCA4466279E153>76 D<B912C018FEF0FFC019F0C601FCC7000113FCD93F F89138001FFF011F04037F727F9538007FF0737E737E190F737E86731380A27313C0A31B E085A21BF0A91BE0A2611BC0A34F13801B0061624F5A4F5A4F5A4F5A4E485A4E90C7FCF0 1FFE943801FFF891B812E096C8FC18F802F8CCFCB3B3A4497E90B5FCB7FCA44C6279E15A >80 D<B812FCEFFFE018FCF0FF80C601FCC7000F13E0D93FF8020013F8011FEE1FFCF007 FF06017F727F737E737E737E86737EA2737EA287A28587A96361A298C8FCA24F5A624F5A A24F5A4F5AF1FF80060390C9FC4E5AF01FF8F0FFE0050F138091B700FCCAFC18E0A202F8 C7EA1FFCEF03FE943800FF80F03FC0727E727E727E727E85727EA2727FA286197FA286A5 86A786A67414E0193FA4736CEB01C0190FA2496C706CEB038090B582B76F903880070073 EBC00E97387FF03C97381FFFF8CD00035B9738007FC05B6479E162>82 D<EC1FF849B5FC010714C090390FE01FF090393F0003F80178EB01FE49EB007F48486E7E 48488149141FD807406E7E01F881486C1407837FA2707EA26C5A6C5A6C5AC9FCA6ED03FF 92B5FC140F027F1303903803FFE0010F1300EB1FF8EB7FE0495A4890C7FC485A485A485A 121F5B123F48481770A3485AA31607A3160FA26C6C141DA26C6CDA38FE13E0001F15706C 6C14E06C6C903A01C07F01C06CB4D90780EB83806C903AC03F003FFF27007FFFFC6D1300 011F01F0EB0FFC01010180EB03F03C417BBF42>97 D<181EEF3FFEEE07FFA4EE000F1703 A21701B3AAEDFF80020F13F8023F13FE9138FFC03F903A03FE0007C1D907F8EB01E1D90F E0EB0071494814394948141D49C8120F01FE15071201484815035B00071601120F5B121F A2485AA3127FA25BA212FFAC127FA37F123FA3121F7F120FA26C6C1503A26C6C15070001 160F7F0000161D017F15396D6CEC71FF6D6C14E1D90FF0D903C113C0D903FCD90F81EBFF 806DB4EB7E019039007FFFFC021F13E00201010091C7FC41657CE349>100 D<4AB4FC021F13F0027F13FC903901FF01FF903A03F8007F80D90FE0EB1FC049486D7E49 486D7E49C76C7E01FE8100016F7E5B00036F7E485AEF7F80485AA2001F17C049153F123F A3007F17E05BA312FF90B8FCA301C0CAFCA8127FA37FA2123FA36C7E18E0120F7F0007EE 01C06C7EEF03806C7E6C6CED07006D150E6D7E6D6C143CD90FF05C6D6C5CD901FEEB03C0 903A00FFC01F8091263FFFFEC7FC020713F8020013C033417DBF3A>I<ED0FF0ED7FFC4A 487E913807F81F91390FE00F8091391F801FC0023FEB3FE091387F007F14FEA2495A0103 EC3FC04AEB1F80EE0F00010791C7FCA25C130FB3A4B712F0A426000FF0C8FCB3B3B0497E EB3FFE003FB6FCA42B657EE428>I<F03F80DA03FC903801FFE091273FFFC00713F091B5 38F01FC1903C01FE07F83E03F8903A07F000FE784948EB7FF0494890393FC001F0494801 1FEB00E049C76C6C1300A201FE6E7E000182A2000382491403A3000782A800035EA36D14 0700015EA200005E017F4A5AA26D6C495A6D6C495A496C49C8FC6E13FE903971FE07F801 70B55AD9F03F13C09026E003FCC9FC000190CBFCA77FA27F6C7E13FF6DB512FEEEFFF06D 15FE6D6F7E6D16E04982017F8201FEC700017FD803F89138001FFED807E0ED03FF484815 004848EE7F8090CA123F48EF1FC0007E170FA219E0481707A7007EEF0FC0A26CEF1F80A2 6C6CEE3F006C6C167E6C6C5ED803F8ED03F86C6C4B5AD8007FED1FC0D93FE0ECFF80D90F FED90FFEC7FC0101B612F0D9003F1480020101F0C8FC3D5E7DBF42>I<133E137F497E48 7F487FA56C5B6C5B6DC7FC133E90C8FCB3EB03C0EA07FF127FA41201EA007FA2133FB3B3 AC497E497EB612E0A41B5F7DDE23>105 D<EB03C0EA07FFB5FCA41201EA007FA2133FB3 B3B3B3AD497E497EB612F0A41C647DE323>108 D<D903C0EB7FE0D807FF903803FFFCB5 010F13FFDB3F0013C00378EB1FE003E06D7E0001D9C1C06D7E27007FC380130302C7C77F D93FCE140102DC81A214F8717E5CA25CA45CB3B3496C4A7F496C4A7FB6D8F003B612C0A4 423F7DBE49>110 D<EDFFE0020713FC023FEBFF809139FF803FE0903A01FC0007F0D907 F0EB01FC49486D7E4948147F49486E7E49C86C7E01FE6F7E48486F7E0003834915030007 83491501000F83001F834981A2003F1880A34848EE7FC0A400FF18E0AC007F18C0A36D16 FF003F1880A3001F18006D5D000F5FA26C6C4B5AA26C6C4B5A00015F6C6C4B5A6D151F6D 6C4A5A6D6C4A5AD90FE002FEC7FCD907F8EB03FCD903FEEB0FF8903A00FF803FE0023FB5 1280020701FCC8FC020013E03B417DBF42>I<9039078003F8D807FFEB0FFFB5013F1380 92387C07C09238F01FE0DA81C013F00001903883803F39007F8700148E133F029CEB1FE0 EE0FC002B8EB030093C7FC14F0A35CA55CB3B1497EEBFFF8B612FCA42C3F7CBE33>114 D<9139FFE00180010FEBFC03017FEBFF079039FF001F8FD803F8EB03DFD807E0EB00FFD8 0F80147F48C8123F161F123E007E150F127C160712FCA316037EA27EA26C7E01E091C7FC EA3FF813FE381FFFF06CEBFF806C14F86C14FF6C15C06C6C14F0011F80010780D9007F7F 02037FDA003F1380030313C0030013E0163F0060ED1FF000E0150F160717F86C1503A216 017EA37E17F0A27E16036C16E06D140717C06DEC0F80D8FCE0EC1F000178143ED8F83E14 FC3AF01FC00FF80107B512E0D8E001148027C0003FF8C7FC2D417DBF34>I<1438A71478 A414F8A31301A31303A21307130F131FA2137F13FF1203000F90B6FCB8FCA3260007F8C8 FCB3AE17E0AE0103EC01C080A2010115806E130313006EEB07006E130E6E6C5A91381FF0 78913807FFF06E5B9138007F802B597FD733>I E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: Letter /setpagedevice where { pop << /PageSize [612 792] >> setpagedevice } { /letter where { pop letter } if } ifelse %%EndPaperSize end HPSdict begin /TargetAnchors 0 dict dup begin end targetdump-hook def end TeXDict begin %%EndSetup %%Page: 1 1 gsave %matrix defaultmatrix setmatrix 90 rotate /stampsize 20 def /Times-Roman findfont stampsize scalefont setfont currentfont /FontBBox get aload pop /pdf@top exch 1000 div stampsize mul def pop /pdf@bottom exch 1000 div stampsize mul def pop 261 -32 moveto currentpoint /pdf@lly exch pdf@bottom add def /pdf@llx exch 2 sub def 0.5 setgray (arXiv:1210.1433v1 [cs.LO] 4 Oct 2012) show currentpoint /pdf@ury exch pdf@top add def /pdf@urx exch 2 add def /pdfmark where{pop}{userdict /pdfmark /cleartomark load put}ifelse [ /H /I /Border [0 0 1] /BS <</S/D/D[2 6]/W 1>> /Color [0 1 1] /Action << /Subtype /URI /URI (http://arxiv.org/abs/1210.1433v1)>> /Subtype /Link /Rect[pdf@llx pdf@lly pdf@urx pdf@ury] /ANN pdfmark grestore TeXDict begin HPSdict begin 1 0 bop 0 0 a SDict begin [/Producer (dvips + Distiller)/Title ()/Subject ()/Creator (LaTeX with hyperref package)/Author ()/Keywords () /DOCINFO pdfmark end 0 0 a 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.1) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin [/Count 0/Dest (section.1) cvn/Title (1 Introduction) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.2) cvn/Title (2 Monotone relations) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.3) cvn/Title (3 Exact squares) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.4) cvn/Title (4 The universal property of \(-\):Pre--3muRel\(Pre\)) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.5) cvn/Title (5 The extension theorem) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.6) cvn/Title (6 Examples) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.7) cvn/Title (7 An Application: Moss's Coalgebraic Logic over Posets) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/Count 0/Dest (section.8) cvn/Title (8 Conclusions) /OUT pdfmark end 0 0 a 0 0 a SDict begin [/PageMode /UseOutlines/Page 1/View [/Fit] /DOCVIEW pdfmark end 0 0 a 0 0 a SDict begin [ {Catalog}<<>> /PUT pdfmark end 0 0 a 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Doc-Start) cvn /DEST pdfmark end 0 0 a Black Black 728 432 a FU(Relation)45 b(Liftings)e(on)h(Preorders) f(and)g(P)l(osets)3172 380 y FT(\003)1643 672 y FS(Marta)32 b(B)-11 b(\023)-38 b(\020lk)m(o)m(v\023)-49 b(a)173 789 y(Institute)33 b(of)f(Computer)h(Science,)g(Academ)m(y)h(of)e(Sciences) i(of)e(the)h(Czec)m(h)h(Republic,)e(Prague)1611 955 y(Alexander)h(Kurz) 2288 918 y FR(y)344 1071 y FS(Departmen)m(t)f(of)g(Computer)h(Science,) h(Univ)m(ersit)m(y)f(of)f(Leicester,)h(United)g(Kingdom)1596 1236 y(Daniela)d(P)m(etri)n(\030)-41 b(san)344 1352 y(Departmen)m(t)32 b(of)g(Computer)h(Science,)h(Univ)m(ersit)m(y)f(of)f(Leicester,)h (United)g(Kingdom)1719 1518 y(Ji)-5 b(\024)-43 b(r)-11 b(\023)-38 b(\020)30 b(V)-8 b(elebil)2183 1482 y FR(z)60 1634 y FS(F)g(acult)m(y)33 b(of)f(Electrical)f(Engineering,)h(Czec)m(h) i(T)-8 b(ec)m(hnical)33 b(Univ)m(ersit)m(y)g(in)f(Prague,)h(Czec)m(h)h (Republic)1622 1830 y(Marc)m(h)g(14,)e(2018)p Black Black 1781 2212 a FQ(Abstract)p Black Black 323 2342 a FP(The)24 b(category)h FO(Rel)q FP(\()p FO(Set)o FP(\))f(of)h(sets)g(and)f (relations)i(can)e(b)r(e)g(describ)r(ed)h(as)g(a)f(category)i(of)f (spans)f(and)g(as)h(the)f(Kleisli)208 2433 y(category)32 b(for)h(the)e(p)r(o)n(w)n(erset)i(monad.)52 b(A)31 b(set-functor)h(can) g(b)r(e)f(lifted)i(to)f(a)g(functor)g(on)f FO(Rel)q FP(\()p FO(Set)o FP(\))h(i\013)f(it)h(preserv)n(es)208 2524 y(w)n(eak)22 b(pullbac)n(ks.)33 b(W)-6 b(e)22 b(sho)n(w)g(that)g(these)g(results)h (extend)e(to)h(the)g(enric)n(hed)g(setting,)h(if)g(w)n(e)g(replace)g (sets)f(b)n(y)f(p)r(osets)i(or)208 2616 y(preorders.)36 b(Preserv)l(ation)27 b(of)g(w)n(eak)f(pullbac)n(ks)g(b)r(ecomes)g (preserv)l(ation)h(of)f(exact)h(lax)f(squares.)36 b(As)26 b(an)g(application)208 2707 y(w)n(e)g(presen)n(t)f(Moss's)j (coalgebraic)g(o)n(v)n(er)d(p)r(osets.)0 2982 y SDict begin H.S end 0 2982 a 0 2982 a SDict begin 18 H.A end 0 2982 a 0 2982 a SDict begin [/View [/XYZ H.V]/Dest (section*.1) cvn /DEST pdfmark end 0 2982 a FN(Con)l(ten)l(ts)0 3164 y FM(1)77 b(In)m(tro)s(duction)3852 3164 y SDict begin H.S end 3852 3164 a FM(2)3900 3164 y SDict begin 12 H.L end 3900 3164 a 3900 3164 a SDict begin [/Subtype /Link/Dest (section.1) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3900 3164 a 0 3347 a FM(2)g(Monotone)30 b(relations)3852 3347 y SDict begin H.S end 3852 3347 a FM(2)3900 3347 y SDict begin 12 H.L end 3900 3347 a 3900 3347 a SDict begin [/Subtype /Link/Dest (section.2) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3900 3347 a 0 3529 a FM(3)77 b(Exact)32 b(squares)3805 3529 y SDict begin H.S end 3805 3529 a FM(10)3901 3529 y SDict begin 12 H.L end 3901 3529 a 3901 3529 a SDict begin [/Subtype /Link/Dest (section.3) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 3529 a 0 3712 a FM(4)77 b(The)32 b(univ)m(ersal)f(prop)s (ert)m(y)i(of)f FL(\()p FK(\000)p FL(\))1359 3724 y FJ(\005)1420 3712 y FL(:)23 b FI(Pre)h FK(\000)-15 b(!)23 b FI(Rel)p FL(\()p FI(Pre)p FL(\))3805 3712 y SDict begin H.S end 3805 3712 a FM(18)3901 3712 y SDict begin 12 H.L end 3901 3712 a 3901 3712 a SDict begin [/Subtype /Link/Dest (section.4) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 3712 a 0 3895 a FM(5)77 b(The)32 b(extension)e(theorem)3805 3895 y SDict begin H.S end 3805 3895 a FM(19)3901 3895 y SDict begin 12 H.L end 3901 3895 a 3901 3895 a SDict begin [/Subtype /Link/Dest (section.5) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 3895 a 0 4077 a FM(6)77 b(Examples)3805 4077 y SDict begin H.S end 3805 4077 a FM(20)3901 4077 y SDict begin 12 H.L end 3901 4077 a 3901 4077 a SDict begin [/Subtype /Link/Dest (section.6) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 4077 a 0 4260 a FM(7)g(An)32 b(Application:)41 b(Moss's)30 b(Coalgebraic)h (Logic)h(o)m(v)m(er)h(P)m(osets)3805 4260 y SDict begin H.S end 3805 4260 a FM(25)3901 4260 y SDict begin 12 H.L end 3901 4260 a 3901 4260 a SDict begin [/Subtype /Link/Dest (section.7) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 4260 a 0 4443 a FM(8)77 b(Conclusions)3805 4443 y SDict begin H.S end 3805 4443 a FM(27)3901 4443 y SDict begin 12 H.L end 3901 4443 a 3901 4443 a SDict begin [/Subtype /Link/Dest (section.8) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 3901 4443 a Black 0 4496 1560 4 v 91 4549 a FH(\003)127 4573 y FG(In)23 b(terms)f(of)h(results)g(and)g(n)n(um)n(b)r(ering,)h(the)f (material)i(has)d(app)r(eared)i(in)g(our)e(CALCO)g(2011)i(pap)r(er)f (of)f(the)h(same)g(title,)i(but)e(some)g(t)n(yp)r(os)0 4652 y(w)n(ere)h(corrected)h(and)f(pro)r(ofs)f(and)h(a)g(small)h(n)n (um)n(b)r(er)f(of)f(further)g(commen)n(ts)i(w)n(ere)f(added.)94 4710 y FH(y)127 4733 y FG(Alexander)h(Kurz)f(ac)n(kno)n(wledges)i(the)f (supp)r(ort)f(of)f(EPSR)n(C,)h(EP/G041296/1.)94 4791 y FH(z)127 4815 y FG(Marta)g(B)-8 b(\023)-27 b(\020lk)n(o)n(v\023)-35 b(a)26 b(and)e(Ji)l(\024)-31 b(r)-8 b(\023)-27 b(\020)24 b(V)-6 b(elebil)26 b(ac)n(kno)n(wledge)h(the)e(supp)r(ort)f(of)f(the)i (gran)n(t)f(No.)f(P202/11/1632)k(of)c(the)i(Czec)n(h)g(Science)h(F)-6 b(oundation.)p Black Black 1929 5400 a FL(1)p Black eop end end %%Page: 2 2 TeXDict begin HPSdict begin 2 1 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.2) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (section.1) cvn /DEST pdfmark end 0 0 a 83 x FN(1)135 b(In)l(tro)t(duction) 0 265 y FL(Relation)25 b(lifting)g([)598 265 y SDict begin H.S end 598 265 a Black FL(Ba)p Black 699 208 a SDict begin H.R end 699 208 a 699 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.barr:rel-alg) cvn H.B /ANN pdfmark end 699 265 a FL(,)750 265 y SDict begin H.S end 750 265 a Black FL(CKW)p Black 959 208 a SDict begin H.R end 959 208 a 959 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.ckw:wpb) cvn H.B /ANN pdfmark end 959 265 a FL(,)1010 265 y SDict begin H.S end 1010 265 a Black FL(HeJ)p Black 1152 208 a SDict begin H.R end 1152 208 a 1152 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.herm-jaco:pred-lift) cvn H.B /ANN pdfmark end 1152 265 a FL(])j(pla)n(ys)d(a)i(crucial)e(role)h(in)h (coalgebraic)c(logic,)i(see)i(eg)g([)2920 265 y SDict begin H.S end 2920 265 a Black FL(Mo)p Black 3038 208 a SDict begin H.R end 3038 208 a 3038 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.moss:cl) cvn H.B /ANN pdfmark end 3038 265 a FL(,)3088 265 y SDict begin H.S end 3088 265 a Black FL(Bal)p Black 3212 207 a SDict begin H.R end 3212 207 a 3212 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.baltag:cmcs00) cvn H.B /ANN pdfmark end 3212 265 a FL(,)3263 265 y SDict begin H.S end 3263 265 a Black FL(V)p Black 3325 208 a SDict begin H.R end 3325 208 a 3325 265 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.venema:coalg-aut) cvn H.B /ANN pdfmark end 3325 265 a FL(].)125 364 y(On)34 b(the)h(one)f(hand,)j(it) d(is)f(used)i(to)f(explain)f(bisim)n(ulation:)45 b(If)35 b FF(T)46 b FL(:)35 b FI(Set)g FK(\000)-14 b(!)34 b FI(Set)h FL(is)f(a)g(functor,)i(then)f(the)g(largest)0 464 y(bisim)n(ulation)19 b(on)25 b(a)f(coalgebra)e FF(\030)27 b FL(:)c FF(X)29 b FK(\000)-14 b(!)23 b FF(T)12 b(X)30 b FL(is)24 b(the)h(largest)d (\014xed)j(p)r(oin)n(t)f(of)h(the)g(op)r(erator)e(\()p FF(\030)17 b FK(\002)c FF(\030)t FL(\))3237 434 y FJ(\000)p FE(1)3339 464 y FK(\016)p 3394 397 61 4 v 13 w FF(T)35 b FL(on)24 b(relations)0 564 y(on)k FF(X)7 b FL(,)28 b(where)p 484 497 V 28 w FF(T)39 b FL(is)27 b(the)i(lifting)d(of)i FF(T)39 b FL(to)28 b FI(Rel)p FL(\()p FI(Set)p FL(\))c FK(\000)-14 b(!)24 b FI(Rel)p FL(\()p FI(Set)p FL(\).)39 b(\(The)29 b(precise)d(meaning)g(of)i(`lifting')e(will)g(b)r(e)i(giv)n (en)f(in)0 663 y(the)h(Extension)e(Theorem)880 663 y SDict begin H.S end 880 663 a Black FL(5.3)p Black 987 610 a SDict begin H.R end 987 610 a 987 663 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.3) cvn H.B /ANN pdfmark end 987 663 a FL(.\))125 763 y(On)39 b(the)g(other)g(hand,)j(Moss's)c (coalgebraic)d(logic)h([)1850 763 y SDict begin H.S end 1850 763 a Black FL(Mo)p Black 1968 706 a SDict begin H.R end 1968 706 a 1968 763 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.moss:cl) cvn H.B /ANN pdfmark end 1968 763 a FL(])j(is)f(giv)n(en)g(b)n(y)h(adding)e(to)i(prop)r(ositional)c (logic)i(a)h(mo)r(dal)0 863 y(op)r(erator)24 b FK(r)p FL(,)i(the)f(seman)n(tics)e(of)i(whic)n(h)f(is)h(giv)n(en)e(b)n(y)i (applying)p 2039 796 61 4 v 23 w FF(T)36 b FL(to)25 b(the)h(forcing)d (relation)g FD(\015)g FK(\022)f FF(X)f FK(\002)13 b(L)p FL(,)26 b(where)f FK(L)h FL(is)e(the)0 962 y(set)k(of)f(form)n(ulas:)34 b(If)28 b FF(\013)23 b FK(2)h FF(T)12 b FL(\()p FK(L)p FL(\),)27 b(then)h FF(x)c FD(\015)f FK(r)p FF(\013)51 b FK(,)g FF(\030)t FL(\()p FF(x)p FL(\))p 1889 896 V 24 w FF(T)11 b FL(\()p FD(\015)p FL(\))24 b FF(\013)p FL(.)125 1062 y(In)f(m)n(uc)n(h)g(the)h(same)e(w)n(a)n(y)h(as)g FI(Set)p FL(-coalgebras)d(capture)j(bisim)n(ulation,)c FI(Pre)p FL(-coalgebras)h(and)k FI(P)n(os)o FL(-coalgebras)c(capture)0 1162 y(sim)n(ulation)25 b([)429 1162 y SDict begin H.S end 429 1162 a Black FL(R)p Black 491 1105 a SDict begin H.R end 491 1105 a 491 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.rutten-rel) cvn H.B /ANN pdfmark end 491 1162 a FL(,)544 1162 y SDict begin H.S end 544 1162 a Black FL(W)-7 b(o)p Black 664 1105 a SDict begin H.R end 664 1105 a 664 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.worrell:cmcs00) cvn H.B /ANN pdfmark end 664 1162 a FL(,)717 1162 y SDict begin H.S end 717 1162 a Black FL(HuJ)p Black 868 1105 a SDict begin H.R end 868 1105 a 868 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.hugh-jaco:simulation) cvn H.B /ANN pdfmark end 868 1162 a FL(,)921 1162 y SDict begin H.S end 921 1162 a Black FL(Kl)p Black 1009 1104 a SDict begin H.R end 1009 1104 a 1009 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.klin:thesis) cvn H.B /ANN pdfmark end 1009 1162 a FL(,)1062 1162 y SDict begin H.S end 1062 1162 a Black FL(L)p Black 1114 1105 a SDict begin H.R end 1114 1105 a 1114 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.levy:simulation) cvn H.B /ANN pdfmark end 1114 1162 a FL(,)1167 1162 y SDict begin H.S end 1167 1162 a Black FL(BK)p Black 1290 1105 a SDict begin H.R end 1290 1105 a 1290 1162 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.bala-kurz:calco11) cvn H.B /ANN pdfmark end 1290 1162 a FL(].)45 b(This)29 b(suggests)f(that,)j(in)f(analogy)d(with)i(the)i FI(Set)p FL(-based)e(case,)h(a)f(coalgebraic)0 1261 y(understanding)i(of)i (logics)d(for)i(sim)n(ulations)c(should)k(deriv)n(e)f(from)g(the)j (study)f(of)f FI(P)n(os)p FL(-functors)g(together)g(with)g(on)h(the)0 1361 y(one)27 b(hand)h(their)f(predicate)f(liftings)f(and)j(on)f(the)i (other)e(hand)h(their)e FK(r)p FL(-op)r(erator.)36 b(The)28 b(study)g(of)g(predicate)e(liftings)f(of)0 1460 y FI(P)n(os)o FL(-functors)c(w)n(as)f(b)r(egun)i(in)f([)975 1460 y SDict begin H.S end 975 1460 a Black FL(KaKuV)p Black 1254 1404 a SDict begin H.R end 1254 1404 a 1254 1460 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kkv:expr) cvn H.B /ANN pdfmark end 1254 1460 a FL(],)i(whereas)d(here)h(w)n(e)g(la)n(y)f (the)h(foundations)f(for)h(the)h FK(r)p FL(-op)r(erator)e(of)h(a)g FI(P)n(os)o FL(-functor.)0 1560 y(In)29 b(order)e(to)i(do)f(this,)h(w)n (e)f(start)g(with)h(the)g(notion)e(of)i(monotone)e(relation)f(for)i (the)h(follo)n(wing)c(reason.)39 b(Let)29 b(\()p FF(X)r(;)14 b FK(\024)p FL(\))28 b(and)0 1660 y(\()p FF(X)108 1630 y FJ(0)131 1660 y FF(;)14 b FK(\024)233 1630 y FJ(0)256 1660 y FL(\))29 b(b)r(e)g(the)g(carriers)c(of)k(t)n(w)n(o)f (coalgebras,)d(with)j(the)i(preorders)c FK(\024)p FF(;)14 b FK(\024)2420 1630 y FJ(0)2471 1660 y FL(enco)r(ding)28 b(the)h(sim)n(ulation)24 b(relations)h(on)k FF(X)0 1759 y FL(and)g FF(X)239 1729 y FJ(0)261 1759 y FL(,)h(resp)r(ectiv)n(ely)-7 b(.)38 b(Then)29 b(a)g(sim)n(ulation)24 b(b)r(et)n(w)n(een)29 b(the)h(t)n(w)n(o)e(systems)f(will)g(b)r(e)i(a)g(relation)d FF(R)g FK(\022)f FF(X)h FK(\002)18 b FF(X)3507 1729 y FJ(0)3559 1759 y FL(suc)n(h)29 b(that)0 1859 y FK(\025)14 b FL(;)27 b FF(R)15 b FL(;)27 b FK(\025)322 1829 y FJ(0)371 1859 y FK(\022)e FF(R)q FL(,)k(that)g(is,)g FF(R)g FL(is)f(a)h (monotone)e(relation.)38 b(Similarly)-7 b(,)24 b FD(\015)29 b FL(will)e(b)r(e)i(a)g(monotone)e(relation.)38 b(T)-7 b(o)29 b(summarise,)0 1959 y(the)35 b(relations)d(w)n(e)i(are)g(in)n (terested)g(in)g(are)g(monotone,)h(whic)n(h)f(enables)f(us)i(to)g(use)f (tec)n(hniques)g(of)h(enric)n(hed)e(category)0 2058 y(theory)27 b(\(of)h(whic)n(h)e(no)i(prior)d(kno)n(wledge)g(is)i(assumed)f(of)h (the)h(reader\).)125 2158 y(F)-7 b(or)23 b(the)i(reasons)d(outlined)h (ab)r(o)n(v)n(e,)h(the)g(purp)r(ose)g(of)g(the)h(pap)r(er)f(is)f(to)i (dev)n(elop)d(the)j(basic)e(theory)g(of)h(relation)e(liftings)0 2257 y(o)n(v)n(er)30 b(preorders)g(and)i(p)r(osets.)49 b(That)32 b(is,)g(w)n(e)f(replace)f(the)j(category)c FI(Set)j FL(of)g(sets)g(and)g(functions)f(b)n(y)g(the)i(category)d FI(Pre)0 2357 y FL(of)j(preorders)e(or)h FI(P)n(os)g FL(of)h(p)r(osets,)i(b)r(oth)e(with)g(monotone)e(\(i.e.)53 b(order-preserving\))28 b(functions.)53 b(Section)32 b(2)h(in)n(tro)r(duces)0 2457 y(notation)c(and)i(sho)n(ws)e(that)i (\(monotone\))e(relations)f(can)i(b)r(e)h(presen)n(ted)f(b)n(y)h(spans) f(and)g(b)n(y)g(arro)n(ws)f(in)g(an)i(appropriate)0 2556 y(Kleisli-categor)o(y)-7 b(.)69 b(Section)39 b(3)h(recalls)d(the)j (notion)f(of)h(exact)g(squares.)73 b(Section)39 b(4)h(c)n(haracterises) d(the)j(inclusion)d(of)0 2656 y(functions)25 b(in)n(to)g(relations)e (\()p FK(\000)o FL(\))987 2668 y FJ(\005)1049 2656 y FL(:)g FI(Pre)g FK(\000)-14 b(!)23 b FI(Rel)p FL(\()p FI(Pre)p FL(\))j(b)n(y)g(a)f(univ)n(ersal)e(prop)r(ert)n(y)i(and)g(sho) n(ws)g(that)h(the)h(relation)c(lifting)p 3840 2589 61 4 v 23 w FF(T)0 2756 y FL(exists)29 b(i\013)h FF(T)42 b FL(satis\014es)29 b(the)i(Bec)n(k-Chev)-5 b(alley-Conditio)o(n)25 b(\(BCC\),)31 b(whic)n(h)f(sa)n(ys)f(that)i FF(T)41 b FL(preserv)n(es)29 b(exact)h(squares.)44 b(The)0 2855 y(BCC)22 b(replaces)d(the)j(familiar)17 b(condition)j(kno)n(wn)h(from)g FI(Rel)o FL(\()p FI(Set)p FL(\),)j(namely)19 b(that)j FF(T)33 b FL(preserv)n(es)20 b(w)n(eak)h(pullbac)n(ks.)32 b(Section)20 b(5)0 2955 y(lists)j(examples)f(of)j(functors)g(\(not\))g (satisfying)d(the)k(BCC)e(and)h(Section)f(6)g(giv)n(es)f(the)j (application)21 b(to)k(Moss's)e(coalgebraic)0 3054 y(logic)i(o)n(v)n (er)h(p)r(osets.)0 3204 y FM(Related)g(w)m(ork.)36 b FL(The)23 b(univ)n(ersal)d(prop)r(ert)n(y)i(of)h(the)h(em)n(b)r(edding) d(of)i(a)g(\(regular\))e(category)g(to)i(the)h(category)d(of)i (relations)0 3303 y(is)j(stated)i(in)f(Theorem)e(2.3)i(of)g([)1031 3303 y SDict begin H.S end 1031 3303 a Black FL(He)p Black 1131 3247 a SDict begin H.R end 1131 3247 a 1131 3303 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.hermida) cvn H.B /ANN pdfmark end 1131 3303 a FL(].)37 b(Theorem)1564 3303 y SDict begin H.S end 1564 3303 a Black FL(4.1)p Black 1670 3250 a SDict begin H.R end 1670 3250 a 1670 3303 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.4.1) cvn H.B /ANN pdfmark end 1670 3303 a 28 w FL(b)r(elo)n(w)26 b(generalizes)e(this)j(in)f(passing)g(from)g(a)h(category)e(to)j(a)f (simple)0 3403 y(2-category)e(of)i(\(pre\)orders.)125 3503 y(Liftings)21 b(of)i(functors)g(to)g(categories)d(of)j(relations)d (within)i(the)i(realm)c(of)j(regular)e(categories)f(ha)n(v)n(e)i(also)f (b)r(een)j(studied)0 3602 y(in)j([)120 3602 y SDict begin H.S end 120 3602 a Black FL(CKW)p Black 330 3546 a SDict begin H.R end 330 3546 a 330 3602 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.ckw:wpb) cvn H.B /ANN pdfmark end 330 3602 a FL(].)0 3748 y SDict begin H.S end 0 3748 a 0 3748 a SDict begin 12 H.A end 0 3748 a 0 3748 a SDict begin [/View [/XYZ H.V]/Dest (section.2) cvn /DEST pdfmark end 0 3748 a 129 x FN(2)135 b(Monotone)45 b(relations)0 4059 y FL(In)29 b(this)g(section)e(w)n(e)i(summarize)d(brie\015y)h(the) j(notion)e(of)h(monotone)e(relations)f(on)j(preorders)e(and)i(w)n(e)f (sho)n(w)h(that)g(their)0 4158 y(resulting)c(2-category)g(can)i(b)r(e)h (p)r(erceiv)n(ed)e(in)h(t)n(w)n(o)g(w)n(a)n(ys:)0 4208 y SDict begin H.S end 0 4208 a 0 4208 a SDict begin 12 H.A end 0 4208 a 0 4208 a SDict begin [/View [/XYZ H.V]/Dest (Item.1) cvn /DEST pdfmark end 0 4208 a Black 101 4324 a FL(1.)p Black 42 w(Monotone)f(relations)f(are)h(certain)g FC(sp)l(ans)7 b FL(,)28 b(called)d FC(two-side)l(d)31 b(discr)l(ete)f(\014br)l(ations)7 b FL(.)0 4374 y SDict begin H.S end 0 4374 a 0 4374 a SDict begin 12 H.A end 0 4374 a 0 4374 a SDict begin [/View [/XYZ H.V]/Dest (Item.2) cvn /DEST pdfmark end 0 4374 a Black 101 4490 a FL(2.)p Black 42 w(Monotone)26 b(relations)f(form)h(a)h FC(Kleisli)k(c)l(ate)l(gory)36 b FL(for)27 b(a)g(certain)f FC(KZ)k(do)l(ctrine)k FL(on)28 b(the)g(category)d(of)j(preorders.)0 4656 y SDict begin H.S end 0 4656 a 0 4656 a SDict begin 12 H.A end 0 4656 a 0 4656 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.1) cvn /DEST pdfmark end 0 4656 a Black FM(De\014nition)j(2.1.)p Black 40 w FL(Giv)n(en)26 b(preorders)g FB(A)46 b FL(and)28 b FB(B)s FL(,)g(a)f FC(monotone)j(r)l(elation)h FF(R)f FC(fr)l(om)g FB(A)49 b FC(to)29 b FB(B)s FL(,)g(denoted)f(b)n(y) 1743 4874 y FB(A)1947 4873 y FA(\025)p 1854 4855 100 4 v 1928 4829 a Fz(R)2053 4853 y Fy(/)p Fx(/)p 1953 4855 V 2078 4874 a FB(B)0 5057 y FL(is)e(a)i(monotone)d(map)i FF(R)d FL(:)f FB(B)931 5027 y Fw(op)1028 5057 y FK(\002)18 b FB(A)41 b FK(\000)-14 b(!)23 b Fv(2)28 b FL(where)f(b)n(y)g Fv(2)h FL(w)n(e)g(denote)f(the)h(t)n(w)n(o-elemen)n(t)d(p)r(oset)i(on)g FK(f)p FL(0)p FF(;)14 b FL(1)p FK(g)26 b FL(with)h(0)c FK(\024)f FL(1.)p Black 1929 5400 a(2)p Black eop end end %%Page: 3 3 TeXDict begin HPSdict begin 3 2 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.3) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a SDict begin H.S end 0 83 a 0 83 a SDict begin 12 H.A end 0 83 a 0 83 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.2) cvn /DEST pdfmark end 0 83 a Black FM(Remark)27 b(2.2.)p Black 36 w FL(Unra)n(v)n(elling)20 b(the)k(de\014nition:)34 b(for)23 b(a)h(binary)e(relation)f FF(R)q FL(,)k FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))22 b(=)h(1)g(means)g(that)h FF(a)g FL(and)g FF(b)g FL(are)f(related)0 183 y(b)n(y)e FF(R)q FL(.)35 b(Monotonicit)n(y)18 b(of)k FF(R)g FL(then)g(means)e (that)i(if)f FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))22 b(=)h(1)e(and)g FF(b)2192 195 y FE(1)2252 183 y FK(\024)i FF(b)e FL(in)g FB(B)k FL(and)c FF(a)i FK(\024)g FF(a)2942 195 y FE(1)3000 183 y FL(in)e FB(A)e FL(,)k(then)f FF(R)q FL(\()p FF(b)3538 195 y FE(1)3574 183 y FF(;)14 b(a)3655 195 y FE(1)3692 183 y FL(\))24 b(=)e(1.)125 349 y(Relations)j(comp)r(ose)g(in)i(the)h (ob)n(vious)d(w)n(a)n(y)-7 b(.)36 b(Tw)n(o)27 b(relations)d(as)j(on)h (the)g(left)f(b)r(elo)n(w)1085 566 y FB(A)1289 565 y FA(\025)p 1196 547 100 4 v 1270 521 a Fz(R)1395 546 y Fy(/)p Fx(/)p 1295 547 V 1420 566 a FB(B)137 b(B)1829 565 y FA(\025)p 1735 547 V 1813 521 a Fz(S)1935 546 y Fy(/)p Fx(/)p 1835 547 V 1959 566 a FB(C)397 b(A)2615 565 y FA(\025)p 2521 547 V 2564 521 a Fz(S)s FJ(\001)p Fz(R)2720 546 y Fy(/)p Fx(/)p 2621 547 V 2745 566 a FB(C)0 749 y FL(comp)r(ose)26 b(to)h(the)h(relation)d(on)i(the)h(righ)n(t)e (ab)r(o)n(v)n(e)g(b)n(y)i(the)g(form)n(ula)1378 944 y SDict begin H.S end 1378 944 a FF(S)c FK(\001)18 b FF(R)q FL(\()p FF(c;)c(a)p FL(\))23 b(=)1850 865 y Fu(_)1881 1044 y Fz(b)1956 944 y FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))k FK(^)h FF(S)5 b FL(\()p FF(c;)14 b(b)p FL(\))2522 944 y SDict begin 12 H.A end 2522 944 a 2522 944 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.1) cvn /DEST pdfmark end 2522 944 a Black 1207 w FL(\(2.1\))p Black 0 1205 a(hence)28 b(the)g(v)-5 b(alidit)n(y)24 b(of)k FF(S)23 b FK(\001)18 b FF(R)q FL(\()p FF(c;)c(a)p FL(\))28 b(is)e(witnessed)h(b)n(y)g(at)h(least)e(one)h FF(b)g FL(suc)n(h)h(that)g(b)r(oth)g FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))27 b(and)g FF(S)5 b FL(\()p FF(c;)14 b(b)p FL(\))28 b(hold.)0 1372 y SDict begin H.S end 0 1372 a 0 1372 a SDict begin 12 H.A end 0 1372 a 0 1372 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.3) cvn /DEST pdfmark end 0 1372 a Black FM(Remark)j(2.3.)p Black 40 w FL(The)d(suprem)n(um)e(in)h(form)n(ula)e(\()1563 1372 y SDict begin H.S end 1563 1372 a Black FL(2.1)p Black 1669 1318 a SDict begin H.R end 1669 1318 a 1669 1372 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.1) cvn H.B /ANN pdfmark end 1669 1372 a FL(\))k(is,)d(in)i(fact,)g(exactly)e(a)h(co)r (end)h(in)f(the)i(sense)e(of)h(enric)n(hed)e(category)0 1471 y(theory)-7 b(,)27 b(see)g([)434 1471 y SDict begin H.S end 434 1471 a Black FL(Ke)p Black 536 1414 a SDict begin H.R end 536 1414 a 536 1471 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kelly:book) cvn H.B /ANN pdfmark end 536 1471 a FL(].)125 1678 y(The)32 b(ab)r(o)n(v)n(e)e(comp)r(osition) e(of)k(relations)d(is)i(asso)r(ciativ)n(e)d(and)k(it)f(has)g(monotone)f (relations)54 b FB(A)3317 1677 y FA(\025)p 3224 1659 100 4 v 3290 1632 a Ft(A)3423 1657 y Fy(/)p Fx(/)p 3323 1659 V 3448 1678 a FB(A)75 b FL(as)32 b(units,)0 1778 y(where)i FB(A)19 b FL(\()p FF(a;)14 b(a)490 1747 y FJ(0)513 1778 y FL(\))35 b(holds)e(i\013)i FF(a)f FK(\024)h FF(a)1133 1747 y FJ(0)1156 1778 y FL(.)58 b(Moreo)n(v)n(er,)34 b(the)h(relations)d(can)i(b)r(e)h(ordered)e(p)r(oin)n(t)n(wise:)49 b FF(R)35 b FK(\000)-14 b(!)35 b FF(S)40 b FL(means)33 b(that)0 1877 y FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))27 b(en)n(tails)e FF(S)5 b FL(\()p FF(b;)14 b(a)p FL(\),)28 b(for)f(ev)n(ery)f FF(a)i FL(and)f FF(b)p FL(.)37 b(Hence)28 b(w)n(e)f(ha)n(v)n(e)f(a)h(2-category)e(of)j(monotone)e(relations)e FI(Rel)o FL(\()p FI(Pre)q FL(\).)0 2043 y SDict begin H.S end 0 2043 a 0 2043 a SDict begin 12 H.A end 0 2043 a 0 2043 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.4) cvn /DEST pdfmark end 0 2043 a Black FM(Remark)41 b(2.4.)p Black 45 w FL(Observ)n(e)35 b(that)i(one)f(can)g(form)f (analogously)d(the)37 b(2-category)d FI(Rel)o FL(\()p FI(P)n(os)o FL(\))j(of)f(monotone)f(relations)e(on)0 2143 y FC(p)l(osets)7 b FL(.)41 b(In)29 b(all)e(what)i(follo)n(ws)d (one)i(can)h(w)n(ork)e(either)h(with)g(preorders)f(or)h(p)r(osets.)41 b(W)-7 b(e)29 b(will)d(fo)r(cus)j(on)g(preorders)e(in)h(the)0 2242 y(rest)c(of)g(the)h(pap)r(er,)g(the)g(mo)r(di\014cations)c(for)j (p)r(osets)g(alw)n(a)n(ys)e(b)r(eing)h(straigh)n(tforw)n(ard.)32 b(Observ)n(e)23 b(that)i(b)r(oth)f FI(Rel)p FL(\()p FI(Pre)p FL(\))h(and)0 2342 y FI(Rel)o FL(\()p FI(P)n(os)p FL(\))j(ha)n(v)n(e)e (the)i(crucial)d(prop)r(ert)n(y:)36 b(The)27 b(only)f(isomorphism)d (2-cells)h(are)j(iden)n(tities.)0 2508 y FM(Remark.)76 b FL(The)25 b(forgetful)e(functor)i FF(V)42 b FL(:)23 b FI(Pre)g FK(\000)-14 b(!)23 b FI(Set)i FL(extends)g(to)f(a)h (faithful)e(functor)i FI(Rel)o FL(\()p FF(V)19 b FL(\))24 b(:)f FI(Rel)o FL(\()p FI(Pre)q FL(\))g FK(\000)-14 b(!)23 b FI(Rel)o FL(\()p FI(Set)q FL(\))0 2608 y(where)k FI(Rel)o FL(\()p FI(Set)q FL(\))h(is)e(the)i(usual)e(category)g(of)i(sets)f(and) g(relations.)0 2745 y SDict begin H.S end 0 2745 a 0 2745 a SDict begin 12 H.A end 0 2745 a 0 2745 a SDict begin [/View [/XYZ H.V]/Dest (subsection.2.1) cvn /DEST pdfmark end 0 2745 a 95 x Fs(2.A)112 b(The)38 b(functor)f FS(\()p FT(\000)p FS(\))1057 2855 y FR(\005)1124 2840 y FS(:)28 b Fr(Pre)g FT(\000)-16 b(!)28 b Fr(Rel)p FS(\()p Fr(Pre)p FS(\))0 2993 y FL(W)-7 b(e)33 b(describ)r(e)e(no)n(w)h(the)g(functor)h (\()p FK(\000)o FL(\))1221 3005 y FJ(\005)1291 2993 y FL(:)e FI(Pre)g FK(\000)-14 b(!)31 b FI(Rel)p FL(\()p FI(Pre)p FL(\))i(and)f(sho)n(w)g(its)f(main)g(prop)r(erties.)49 b(The)32 b(case)g(of)g(p)r(osets)g(is)0 3093 y(completely)24 b(analogous.)34 b(F)-7 b(or)27 b(a)g(monotone)f(map)g FF(f)32 b FL(:)23 b FB(A)42 b FK(\000)-14 b(!)23 b FB(B)31 b FL(de\014ne)d(t)n(w)n(o)f(relations)1287 3328 y FB(A)1491 3327 y FA(\025)p 1398 3309 100 4 v 1464 3271 a Fz(f)1496 3279 y Fq(\005)1597 3307 y Fy(/)p Fx(/)p 1498 3309 V 1622 3328 a FB(B)502 b(B)2396 3327 y FA(\025)p 2303 3309 V 2366 3271 a Fz(f)2405 3246 y Fq(\005)2502 3307 y Fy(/)p Fx(/)p 2402 3309 V 2527 3328 a FB(A)0 3511 y FL(b)n(y)27 b(the)h(form)n(ulas)d FF(f)637 3523 y FJ(\005)674 3511 y FL(\()p FF(b;)14 b(a)p FL(\))24 b(=)e FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))28 b(and)g FF(f)1515 3480 y FJ(\005)1552 3511 y FL(\()p FF(a;)14 b(b)p FL(\))23 b(=)g FB(B)s FL(\()p FF(f)9 b(a;)14 b(b)p FL(\).)0 3677 y SDict begin H.S end 0 3677 a 0 3677 a SDict begin 12 H.A end 0 3677 a 0 3677 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.5) cvn /DEST pdfmark end 0 3677 a Black FM(Lemma)30 b(2.5.)p Black 40 w FC(F)-6 b(or)30 b(every)g FF(f)i FL(:)23 b FB(A)42 b FK(\000)-15 b(!)23 b FB(B)34 b FC(in)c FI(Pre)g FC(ther)l(e)g(is)g(an)g(adjunction)g(in)g FI(Rel)o FL(\()p FI(Pre)q FL(\))1565 3872 y FF(f)1606 3884 y FJ(\005)1667 3872 y FK(a)23 b FF(f)1791 3842 y FJ(\005)1852 3872 y FL(:)g FB(B)2095 3871 y FA(\025)p 2002 3853 100 4 v 2201 3851 a Fy(/)p Fx(/)p 2101 3853 V 2226 3872 a FB(A)43 b FF(:)p Black 0 4066 a FC(Pr)l(o)l(of.)p Black 43 w FL(This)27 b(is)f(easy:)36 b(observ)n(e)26 b(that)i(if)f FB(A)19 b FL(\()p FF(a;)14 b(a)1543 4036 y FJ(0)1566 4066 y FL(\))23 b(=)g(1,)k(then)498 4266 y FF(f)548 4231 y FJ(\005)604 4266 y FK(\001)19 b FF(f)687 4278 y FJ(\005)724 4266 y FL(\()p FF(a;)14 b(a)881 4231 y FJ(0)905 4266 y FL(\))23 b(=)1048 4187 y Fu(_)1079 4366 y Fz(b)1154 4266 y FF(f)1204 4231 y FJ(\005)1241 4266 y FL(\()p FF(a)1317 4231 y FJ(0)1341 4266 y FF(;)14 b(b)p FL(\))k FK(^)h FF(f)1579 4278 y FJ(\005)1617 4266 y FL(\()p FF(b;)14 b(a)p FL(\))23 b(=)1909 4187 y Fu(_)1940 4366 y Fz(b)2015 4266 y FB(B)s FL(\()p FF(f)9 b(a)2219 4231 y FJ(0)2242 4266 y FF(;)14 b(b)p FL(\))19 b FK(^)f FB(B)s FL(\()p FF(b;)c(f)9 b(a)p FL(\))24 b(=)e FB(B)s FL(\()p FF(f)9 b(a;)14 b(f)9 b(a)3194 4231 y FJ(0)3218 4266 y FL(\))23 b(=)g(1)0 4536 y(since)j FF(f)37 b FL(is)26 b(a)h(monotone)f(map.)36 b(Hence)28 b FF(\021)1324 4506 y Fz(f)1390 4536 y FL(:)23 b FB(A)42 b FK(\000)-14 b(!)23 b FF(f)1752 4506 y FJ(\005)1808 4536 y FK(\001)18 b FF(f)1890 4548 y FJ(\005)1956 4536 y FL(holds.)125 4635 y(F)-7 b(or)27 b(the)g(comparison)d FF(f)896 4647 y FJ(\005)953 4635 y FK(\001)18 b FF(f)1044 4605 y FJ(\005)1105 4635 y FK(\000)-14 b(!)23 b FB(B)s FL(,)28 b(supp)r(ose)f(that)757 4830 y FF(f)798 4842 y FJ(\005)854 4830 y FK(\001)19 b FF(f)946 4796 y FJ(\005)983 4830 y FL(\()p FF(b;)14 b(b)1124 4796 y FJ(0)1147 4830 y FL(\))23 b(=)1290 4751 y Fu(_)1318 4925 y Fz(a)1396 4830 y FF(f)1437 4842 y FJ(\005)1475 4830 y FL(\()p FF(b;)14 b(a)p FL(\))k FK(^)h FF(f)1798 4796 y FJ(\005)1836 4830 y FL(\()p FF(a;)14 b(b)1985 4796 y FJ(0)2008 4830 y FL(\))23 b(=)2151 4751 y Fu(_)2179 4925 y Fz(a)2257 4830 y FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))19 b FK(^)f FB(B)s FL(\()p FF(f)9 b(a;)14 b(b)2935 4796 y FJ(0)2959 4830 y FL(\))23 b(=)g(1)0 5087 y(and)k(use)h(the)g(transitivit)n(y)c(of)j(the)h(order)f(on)g FB(B)k FL(to)d(conclude)e(that)i FB(B)s FL(\()p FF(b;)14 b(b)2398 5057 y FJ(0)2421 5087 y FL(\))24 b(=)e(1.)p Black 1929 5400 a(3)p Black eop end end %%Page: 4 4 TeXDict begin HPSdict begin 4 3 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.4) cvn /DEST pdfmark end -8 -8 a Black Black 125 83 a FL(It)27 b(is)g(no)n(w)g(easy)g(to)g(sho)n(w)g(that)h(the)g (triangle)c(equalities)1073 326 y FF(f)1114 338 y FJ(\005)1206 269 y Fz(f)1238 277 y Fq(\005)1273 269 y Fz(\021)1309 244 y Fp(f)1376 305 y Fy(/)p Fx(/)p 1177 307 200 4 v 1490 554 a FA(I)1459 533 y(I)1428 512 y(I)1397 491 y(I)1366 469 y(I)1336 448 y(I)1305 427 y(I)1274 406 y(I)1243 385 y(I)1212 364 y(I)1182 343 y(I)1480 568 y(I)1450 547 y(I)1419 525 y(I)1388 504 y(I)1357 483 y(I)1326 462 y(I)1295 441 y(I)1265 420 y(I)1234 399 y(I)1203 377 y(I)1172 356 y(I)1401 326 y FF(f)1442 338 y FJ(\005)1498 326 y FK(\001)19 b FF(f)1590 296 y FJ(\005)1646 326 y FK(\001)f FF(f)1728 338 y FJ(\005)1609 488 y Fz(")1640 463 y Fp(f)1677 488 y Fz(f)1709 496 y Fq(\005)1584 567 y Fy(\017)p Fx(\017)p 1582 567 4 200 v 1544 649 a FF(f)1585 661 y FJ(\005)1874 461 y FL(and)2116 326 y FF(f)2166 296 y FJ(\005)2254 269 y Fz(\021)2290 244 y Fp(f)2328 269 y Fz(f)2367 244 y Fq(\005)2428 305 y Fy(/)p Fx(/)p 2229 307 200 4 v 2542 552 a FA(I)2511 532 y(I)2480 511 y(I)2449 490 y(I)2418 469 y(I)2387 449 y(I)2357 428 y(I)2326 407 y(I)2295 386 y(I)2264 366 y(I)2233 345 y(I)2532 566 y(I)2501 545 y(I)2470 524 y(I)2440 504 y(I)2409 483 y(I)2378 462 y(I)2347 442 y(I)2316 421 y(I)2285 400 y(I)2255 379 y(I)2224 359 y(I)2453 326 y FF(f)2503 296 y FJ(\005)2559 326 y FK(\001)g FF(f)2641 338 y FJ(\005)2698 326 y FK(\001)g FF(f)2789 296 y FJ(\005)2665 488 y Fz(f)2704 463 y Fq(\005)2738 488 y Fz(")2769 463 y Fp(f)2640 567 y Fy(\017)p Fx(\017)p 2638 567 4 200 v 2596 649 a FF(f)2646 619 y FJ(\005)0 839 y FL(hold)26 b(and)i(they)g(witness)e(the)i(adjunction)f FF(f)1421 851 y FJ(\005)1482 839 y FK(a)c FF(f)1606 809 y FJ(\005)1643 839 y FL(.)p 3839 839 4 57 v 3843 786 50 4 v 3843 839 V 3893 839 4 57 v 0 1005 a SDict begin H.S end 0 1005 a 0 1005 a SDict begin 12 H.A end 0 1005 a 0 1005 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.6) cvn /DEST pdfmark end 0 1005 a Black FM(Remark)33 b(2.6.)p Black 42 w FL(Left)d(adjoin)n(t)f(morphisms)d(in)j FI(Rel)o FL(\()p FI(Pre)q FL(\))h(can)g(b)r(e)g(c)n(haracterized)d(as)i(exactly)f(those) h(of)h(the)g(form)f FF(f)3733 1017 y FJ(\005)3801 1005 y FL(for)0 1117 y(some)i(monotone)g(map)g FF(f)9 b FL(.)52 b(Therefore,)32 b(if)57 b FF(L)23 b FK(a)g FF(R)g FL(:)h FB(B)1910 1116 y FA(\025)p 1816 1098 100 4 v 2015 1096 a Fy(/)p Fx(/)p 1916 1098 V 2040 1117 a FB(A)77 b FL(in)31 b FI(Rel)p FL(\()p FI(Pre)p FL(\),)k(then)e(there)f(exists)f(a)h (monotone)f(map)0 1217 y FF(f)h FL(:)23 b FB(A)41 b FK(\000)-14 b(!)23 b FB(B)32 b FL(suc)n(h)27 b(that)h FF(f)899 1229 y FJ(\005)960 1217 y FL(=)22 b FF(L)28 b FL(and)f FF(f)1343 1187 y FJ(\005)1404 1217 y FL(=)22 b FF(R)q FL(.)37 b(Moreo)n(v)n(er,) 25 b FF(f)36 b FL(is)27 b(uniquely)e(determined)h(b)n(y)i FF(L;)14 b(R)27 b FL(i\013)g FB(B)32 b FL(is)26 b(a)i(p)r(oset.)125 1317 y(T)-7 b(o)25 b(pro)n(v)n(e)f(the)i(claim,)e(denote)h(b)n(y)h FF(\021)g FL(:)d FB(A)42 b FK(\000)-14 b(!)23 b FF(R)16 b FK(\001)f FF(L)25 b FL(the)h(unit)g(and)f(b)n(y)h FF(")d FL(:)g FF(L)14 b FK(\001)i FF(R)23 b FK(\000)-14 b(!)23 b FB(B)30 b FL(the)c(counit)f(of)h FF(L)c FK(a)h FF(R)q FL(.)36 b(First)0 1416 y(w)n(e)27 b(pro)n(v)n(e)f(that)i(for)f(ev)n (ery)f FF(a)i FL(there)f(is)g(a)g FF(b)1345 1428 y FE(0)1410 1416 y FL(suc)n(h)g(that)1549 1599 y FF(R)q FL(\()p FF(a;)14 b(b)1762 1611 y FE(0)1799 1599 y FL(\))19 b FK(^)g FF(L)p FL(\()p FF(b)2049 1611 y FE(0)2085 1599 y FF(;)14 b(a)p FL(\))23 b(=)g(1)0 1781 y(and)k(that)h FF(b)377 1793 y FE(0)442 1781 y FL(is)e(unique)h(up)h(to)g(isomorphism:)0 1831 y SDict begin H.S end 0 1831 a 0 1831 a SDict begin 12 H.A end 0 1831 a 0 1831 a SDict begin [/View [/XYZ H.V]/Dest (Item.3) cvn /DEST pdfmark end 0 1831 a Black 101 1947 a FL(1.)p Black 42 w(Due)g(to)f FF(\021)k FL(there)c(is)g(at)g (least)g(one)g FF(b)g FL(suc)n(h)g(that)1690 2130 y FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))19 b FK(^)f FF(L)p FL(\()p FF(b;)c(a)p FL(\))23 b(=)g(1)208 2313 y(holds:)35 b(since)26 b FB(A)19 b FL(\()p FF(a;)14 b(a)p FL(\))23 b(=)g(1,)k(it)g(is)g(the)h (case)f(that)g FF(R)20 b FK(\001)e FF(L)p FL(\()p FF(a;)c(a)p FL(\))23 b(=)g(1.)0 2367 y SDict begin H.S end 0 2367 a 0 2367 a SDict begin 12 H.A end 0 2367 a 0 2367 a SDict begin [/View [/XYZ H.V]/Dest (Item.4) cvn /DEST pdfmark end 0 2367 a Black 101 2479 a FL(2.)p Black 42 w(Supp)r(ose)k (that)1103 2578 y FF(R)q FL(\()p FF(a;)14 b(b)1316 2590 y FE(1)1352 2578 y FL(\))19 b FK(^)g FF(L)p FL(\()p FF(b)1602 2590 y FE(1)1639 2578 y FF(;)14 b(a)p FL(\))23 b(=)f(1)83 b(and)g FF(R)q FL(\()p FF(a;)14 b(b)2417 2590 y FE(2)2453 2578 y FL(\))19 b FK(^)g FF(L)p FL(\()p FF(b)2703 2590 y FE(2)2739 2578 y FF(;)14 b(a)p FL(\))24 b(=)e(1)208 2728 y(hold.)35 b(Therefore)27 b(the)h(equalities)1103 2911 y FF(R)q FL(\()p FF(a;)14 b(b)1316 2923 y FE(1)1352 2911 y FL(\))19 b FK(^)g FF(L)p FL(\()p FF(b)1602 2923 y FE(2)1639 2911 y FF(;)14 b(a)p FL(\))23 b(=)f(1)83 b(and)g FF(R)q FL(\()p FF(a;)14 b(b)2417 2923 y FE(2)2453 2911 y FL(\))19 b FK(^)g FF(L)p FL(\()p FF(b)2703 2923 y FE(1)2739 2911 y FF(;)14 b(a)p FL(\))24 b(=)e(1)208 3093 y(hold)k(as)i(w)n(ell.)36 b(Then,)28 b(due)g(to)g FF(")p FL(,)g(w)n(e)g(ha)n(v)n(e)f(that)h FB(B)s FL(\()p FF(b)1927 3105 y FE(1)1965 3093 y FF(;)14 b(b)2038 3105 y FE(2)2075 3093 y FL(\))24 b(=)f(1)28 b(and)g FB(B)s FL(\()p FF(b)2597 3105 y FE(2)2635 3093 y FF(;)14 b(b)2708 3105 y FE(1)2745 3093 y FL(\))24 b(=)f(1.)76 b(In)28 b(other)g(w)n(ords,)f(w)n(e)g(ha)n(v)n(e)208 3193 y FF(b)244 3205 y FE(1)304 3193 y FK(\024)c FF(b)428 3205 y FE(2)493 3193 y FL(and)28 b FF(b)691 3205 y FE(2)752 3193 y FK(\024)23 b FF(b)876 3205 y FE(1)913 3193 y FL(,)28 b(that)h(is,)e FF(b)1288 3205 y FE(1)1348 3171 y FK(\030)1348 3197 y FL(=)1437 3193 y FF(b)1473 3205 y FE(2)1538 3193 y FL(and,)h(if)f FB(B)32 b FL(is)27 b(a)g(p)r(oset)h(then,)57 b(using)27 b(an)n(tisymmetry)-7 b(,)24 b(w)n(e)k(conclude)f(that)208 3292 y FF(b)244 3304 y FE(1)303 3292 y FL(=)c FF(b)427 3304 y FE(2)464 3292 y FL(.)0 3458 y(De\014ne)32 b FF(f)9 b(a)29 b FL(=)h FF(b)515 3470 y FE(0)551 3458 y FL(,)j(whic)n(h)e (determines)e FF(f)40 b FL(uniquely)30 b(i\013)h FB(B)k FL(is)c(a)g(p)r(oset.)49 b(That)31 b(the)h(assignmen)n(t)d FF(a)g FK(7!)h FF(f)9 b(a)31 b FL(is)g(monotone,)0 3558 y(follo)n(ws)24 b(from)i(the)i(existence)e(of)h FF(\021)s FL(.)37 b(Finally)-7 b(,)24 b(w)n(e)j(need)g(to)g(pro)n(v)n(e)f FF(L)c FL(=)h FF(f)2308 3570 y FJ(\005)2346 3558 y FL(,)k(that)h(is,)e FF(L)p FL(\()p FF(b;)14 b(a)p FL(\))23 b(=)f FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))28 b(for)f(all)d FF(b;)14 b(a)p FL(.)37 b(W)-7 b(e)0 3658 y(kno)n(w)25 b FF(L)p FL(\()p FF(f)9 b(a;)14 b(a)p FL(\))26 b(and)f FF(R)q FL(\()p FF(a;)14 b(f)9 b(a)p FL(\))26 b(b)n(y)g(de\014nition)e(of)i FF(f)9 b FL(.)36 b(Supp)r(ose)26 b FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\),)27 b(then)f FF(L)p FL(\()p FF(b;)14 b(a)p FL(\))26 b(follo)n(ws)d(b)n(y)i(monotonicit)n(y)e(of)i FF(L)p FL(.)0 3757 y(Con)n(v)n(ersely)-7 b(,)30 b(supp)r(ose)i FF(L)p FL(\()p FF(b;)14 b(a)p FL(\).)49 b(Using)31 b FF(")f FL(:)g FF(L)21 b FK(\001)g FF(R)31 b FK(\000)-14 b(!)30 b FB(B)s FL(,)k(w)n(e)e(ha)n(v)n(e)2266 3695 y Fu(W)2335 3782 y Fz(a)2389 3757 y FF(L)p FL(\()p FF(b;)14 b(a)p FL(\))21 b FK(^)h FF(R)q FL(\()p FF(a;)14 b(b)2938 3727 y FJ(0)2961 3757 y FL(\))30 b FK(\024)g FB(B)s FL(\()p FF(b;)14 b(b)3337 3727 y FJ(0)3360 3757 y FL(\))33 b(and)f(c)n(ho)r (osing)0 3857 y FF(b)36 3827 y FJ(0)82 3857 y FL(=)23 b FF(f)9 b(a)p FL(,)27 b(w)n(e)g(get)g(1)c(=)g FF(L)p FL(\()p FF(b;)14 b(a)p FL(\))k FK(^)g FF(R)q FL(\()p FF(a;)c(f)9 b(a)p FL(\))23 b FK(\024)g FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\).)p 3839 3857 4 57 v 3843 3804 50 4 v 3843 3857 V 3893 3857 4 57 v 125 4023 a(Observ)n(e)39 b(that)i(if)g FF(f)54 b FK(\000)-14 b(!)45 b FF(g)s FL(,)f(then)e FF(f)1368 4035 y FJ(\005)1451 4023 y FK(\000)-14 b(!)45 b FF(g)1670 4035 y FJ(\005)1749 4023 y FL(holds.)76 b(F)-7 b(or)41 b(if)f FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))46 b(=)f(1)c(then)g FB(B)s FL(\()p FF(b;)14 b(g)s(a)p FL(\))46 b(=)f(1)c(holds)e(b)n(y)0 4123 y(transitivit)n(y)-7 b(,)29 b(since)i FF(f)9 b(a)29 b FK(\024)g FF(g)s(a)i FL(holds.)48 b(Moreo)n(v)n(er,)30 b(taking)g(the)i(lo)n(w)n(er)d(diamond)g(clearly)g (maps)h(an)h(iden)n(tit)n(y)f(monotone)0 4276 y(map)36 b FC(id)271 4288 y Ft(A)379 4276 y FL(:)j FB(A)58 b FK(\000)-14 b(!)39 b FB(A)56 b FL(to)37 b(the)g(iden)n(tit)n(y)f(monotone)f (relation)59 b FB(A)2502 4275 y FA(\025)p 2284 4257 225 4 v 2346 4216 a Ft(A)13 b FE(=\()p Fw(id)2551 4225 y Fo(A)2609 4216 y FE(\))2635 4224 y Fq(\005)2732 4255 y Fy(/)p Fx(/)p 2508 4257 V 2757 4276 a FB(A)43 b FL(.)66 b(F)-7 b(urther,)40 b(taking)35 b(the)j(lo)n(w)n(er)0 4375 y(diamond)25 b(preserv)n(es)h(comp)r(osition:)799 4570 y(\()p FF(g)c FK(\001)c FF(f)9 b FL(\))1016 4582 y FJ(\005)1054 4570 y FL(\()p FF(c;)14 b(a)p FL(\))24 b(=)e FB(C)14 b FL(\()p FF(c;)g(g)s(f)9 b(a)p FL(\))23 b(=)1800 4491 y Fu(_)1831 4670 y Fz(b)1906 4570 y FB(C)14 b FL(\()p FF(c;)g(g)s(b)p FL(\))k FK(^)h FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))23 b(=)g FF(g)2743 4582 y FJ(\005)2799 4570 y FK(\001)c FF(f)2882 4582 y FJ(\005)2919 4570 y FL(\()p FF(c;)14 b(a)p FL(\))0 4832 y(Hence)38 b(w)n(e)g(ha)n(v)n(e)e(a)i(functor)g(\()p FK(\000)p FL(\))1099 4844 y FJ(\005)1177 4832 y FL(:)j FI(Pre)f FK(\000)-14 b(!)40 b FI(Rel)p FL(\()p FI(Pre)p FL(\))f(enric)n(hed)d(in)h (preorders.)66 b(Moreo)n(v)n(er,)38 b(\()p FK(\000)p FL(\))3311 4844 y FJ(\005)3387 4832 y FL(is)f FC(lo)l(c)l(al)t(ly)k (ful)t(ly)0 4931 y(faithful)9 b FL(,)29 b(i.e.,)e FF(f)512 4943 y FJ(\005)573 4931 y FK(\000)-15 b(!)23 b FF(g)769 4943 y FJ(\005)835 4931 y FL(holds)j(i\013)h FF(f)32 b FK(\000)-14 b(!)23 b FF(g)30 b FL(holds.)p Black 1929 5400 a(4)p Black eop end end %%Page: 5 5 TeXDict begin HPSdict begin 5 4 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.5) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (subsection.2.2) cvn /DEST pdfmark end 0 0 a 83 x Fs(2.B)112 b Fr(Rel)p FS(\()p Fr(Pre)p FS(\))38 b Fs(as)g(a)g(Kleisli)g(category)0 236 y FL(The)h(2-functor)f(\()p FK(\000)p FL(\))680 248 y FJ(\005)761 236 y FL(:)k FI(Pre)h FK(\000)-15 b(!)43 b FI(Rel)o FL(\()p FI(Pre)p FL(\))d(is)e(a)h FC(pr)l(o)l(arr)l(ow)i(e)l (quipment)f(with)h(p)l(ower)g(obje)l(cts)47 b FL(in)38 b(the)i(sense)e(of)h(Sec-)0 336 y(tion)29 b(2.5)h([)333 336 y SDict begin H.S end 333 336 a Black FL(MR)-9 b(W)p Black 546 279 a SDict begin H.R end 546 279 a 546 336 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.marmolejo+rosebrugh+wood) cvn H.B /ANN pdfmark end 546 336 a FL(].)45 b(This)29 b(means)g(that)i(\()p FK(\000)p FL(\))1398 348 y FJ(\005)1466 336 y FL(has)f(a)g(righ)n(t)f (adjoin)n(t)g(\()p FK(\000)o FL(\))2305 306 y FJ(y)2371 336 y FL(suc)n(h)h(that)g(the)h(resulting)d(2-monad)g(on)i FI(Pre)g FL(is)0 436 y(a)e(KZ)g(do)r(ctrine)f(and)i FI(Rel)o FL(\()p FI(Pre)q FL(\))f(is)g(\(up)h(to)f(equiv)-5 b(alence\))27 b(the)h(corresp)r(onding)e(Kleisli)e(2-category)-7 b(.)37 b(All)27 b(of)h(the)h(follo)n(wing)0 535 y(results)d(are)h(pro)n(v)n (ed)f(in)h(the)h(pap)r(er)f([)1169 535 y SDict begin H.S end 1169 535 a Black FL(MR)-9 b(W)p Black 1382 478 a SDict begin H.R end 1382 478 a 1382 535 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.marmolejo+rosebrugh+wood) cvn H.B /ANN pdfmark end 1382 535 a FL(],)28 b(w)n(e)f(summarize)d(it)j(here)g(for)g(further)h (reference.)125 635 y(The)f(2-functor)g(\()p FK(\000)p FL(\))782 605 y FJ(y)844 635 y FL(w)n(orks)f(as)h(follo)n(ws:)0 689 y SDict begin H.S end 0 689 a 0 689 a SDict begin 12 H.A end 0 689 a 0 689 a SDict begin [/View [/XYZ H.V]/Dest (Item.5) cvn /DEST pdfmark end 0 689 a Black 101 801 a FL(1.)p Black 42 w(On)g(ob)5 b(jects,)27 b FB(A)739 771 y FJ(y)796 801 y FL(=)c([)p FB(A)993 771 y Fw(op)1070 801 y FF(;)14 b Fv(2)p FL(],)28 b(the)g(lo)n(w)n(ersets)d(on)i FB(A)19 b FL(,)28 b(ordered)e(b)n(y)h(inclusion.)0 855 y SDict begin H.S end 0 855 a 0 855 a SDict begin 12 H.A end 0 855 a 0 855 a SDict begin [/View [/XYZ H.V]/Dest (Item.6) cvn /DEST pdfmark end 0 855 a Black 101 967 a FL(2.)p Black 42 w(F)-7 b(or)37 b(a)h(relation)d FF(R)k FL(from)e FB(A)56 b FL(to)38 b FB(B)s FL(,)k(the)d(functor)f FF(R)1966 937 y FJ(y)2041 967 y FL(:)i([)p FB(A)2213 937 y Fw(op)2291 967 y FF(;)14 b Fv(2)p FL(])40 b FK(\000)-14 b(!)41 b FL([)p FB(B)2713 937 y Fw(op)2791 967 y FF(;)14 b Fv(2)p FL(])38 b(is)g(de\014ned)g(as)f(the)i(left)f(Kan)208 1066 y(extension)29 b(of)i FF(a)e FK(7!)g FF(R)q FL(\()p FK(\000)p FF(;)14 b(a)p FL(\))31 b(along)e(the)i(Y)-7 b(oneda)31 b(em)n(b)r(edding)e Fv(y)2298 1078 y Ft(A)2397 1066 y FL(:)g FB(A)48 b FK(\000)-14 b(!)29 b FL([)p FB(A)2835 1036 y Fw(op)2913 1066 y FF(;)14 b Fv(2)p FL(].)48 b(This)30 b(can)h(b)r(e)g(expressed)208 1166 y(b)n(y)c(the)h(form)n(ula:)1501 1278 y FF(R)1565 1243 y FJ(y)1600 1278 y FL(\()p FF(W)12 b FL(\))23 b(=)g FF(b)f FK(7!)2029 1199 y Fu(_)2058 1373 y Fz(a)2136 1278 y FF(W)12 b(a)18 b FK(^)h FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))208 1510 y(i.e.,)26 b FF(b)i FL(is)e(in)h(the)h (lo)n(w)n(erset)d FF(R)1134 1480 y FJ(y)1168 1510 y FL(\()p FF(W)12 b FL(\))28 b(i\013)g(there)f(exists)f FF(a)i FL(in)f FF(W)39 b FL(suc)n(h)27 b(that)h FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))28 b(holds.)0 1676 y(It)g(is)f(easy)g(to)h(pro)n (v)n(e)e(that)j(\()p FK(\000)p FL(\))993 1646 y FJ(y)1056 1676 y FL(is)d(a)i(2-functor)f(and)h(that)g(\()p FK(\000)p FL(\))2038 1646 y FJ(y)2097 1676 y FK(a)23 b FL(\()p FK(\000)p FL(\))2300 1688 y FJ(\005)2366 1676 y FL(is)k(a)h (2-adjunction)e(of)i(a)g(KZ)f(t)n(yp)r(e.)38 b(The)28 b(latter)0 1776 y(means)e(that)i(if)f(w)n(e)g(denote)h(b)n(y)1806 1875 y SDict begin H.S end 1806 1875 a FL(\()p Fv(L)p FF(;)14 b Fv(y)p FF(;)g Fv(m)p FL(\))2094 1875 y SDict begin 12 H.A end 2094 1875 a 2094 1875 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.2) cvn /DEST pdfmark end 2094 1875 a Black 1635 w FL(\(2.2\))p Black 0 2025 a(the)29 b(resulting)d(2-monad)h(on)h FI(Pre)q FL(,)h(then)g(w)n(e)g(obtain)e (the)i(string)f(of)g(adjunctions)g Fv(L)p FL(\()p Fv(y)2736 2037 y Ft(A)2806 2025 y FL(\))d FK(a)g Fv(m)2999 2037 y Ft(A)3094 2025 y FK(a)g Fv(y)3209 2037 y Fn(L)p Ft(A)3318 2025 y FL(,)k(see)g([)3529 2037 y SDict begin H.S end 3529 2037 a Black -12 x FL(M)3605 2037 y FE(1)p Black 3642 1968 a SDict begin H.R end 3642 1968 a 3642 2025 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.marmolejo1) cvn H.B /ANN pdfmark end 3642 2025 a FL(],)g([)3740 2037 y SDict begin H.S end 3740 2037 a Black -12 x FL(M)3816 2037 y FE(2)p Black 3854 1968 a SDict begin H.R end 3854 1968 a 3854 2025 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.marmolejo2) cvn H.B /ANN pdfmark end 3854 2025 a FL(],)0 2124 y(for)e(more)f(details.)125 2224 y(The)f(unit)h(of)f(the)h(ab)r(o)n(v)n (e)f(KZ)g(do)r(ctrine)f(is)h(the)h(Y)-7 b(oneda)25 b(em)n(b)r(edding)f Fv(y)2371 2236 y Ft(A)2464 2224 y FL(:)f FB(A)42 b FK(\000)-14 b(!)23 b FL([)p FB(A)2885 2194 y Fw(op)2962 2224 y FF(;)14 b Fv(2)p FL(])26 b(and)g(the)g(m)n(ultiplication)0 2324 y Fv(m)60 2336 y Fz(A)148 2324 y FL(:)33 b([[)p FB(A)336 2294 y Fw(op)414 2324 y FF(;)14 b Fv(2)p FL(])520 2294 y Fw(op)598 2324 y FF(;)g Fv(2)p FL(])33 b FK(\000)-14 b(!)34 b FL([)p FB(A)1014 2294 y Fw(op)1091 2324 y FF(;)14 b Fv(2)p FL(])34 b(is)f(the)i(left)e(Kan)h(extension)e(of)i(iden)n(tit) n(y)e(on)i([)p FB(A)2826 2294 y Fw(op)2904 2324 y FF(;)14 b Fv(2)p FL(])34 b(along)e Fv(y)3311 2339 y FE([)p Ft(A)3396 2322 y Fm(op)3452 2339 y Fz(;)p Fn(2)p FE(])3531 2324 y FL(.)56 b(In)34 b(more)0 2423 y(detail:)1346 2523 y Fv(m)1406 2535 y Ft(A)1475 2523 y FL(\()p FB(W)23 b FL(\))h(=)e FF(a)h FK(7!)1913 2444 y Fu(_)1924 2622 y Fz(W)2019 2523 y FB(W)g FL(\()p FF(W)12 b FL(\))19 b FK(^)g FF(W)12 b FL(\()p FF(a)p FL(\))0 2751 y(where)35 b FB(W)58 b FL(is)34 b(in)g([[)p FB(A)700 2721 y Fw(op)778 2751 y FF(;)14 b Fv(2)p FL(])884 2721 y Fw(op)962 2751 y FF(;)g Fv(2)p FL(])35 b(and)g FF(W)48 b FL(is)34 b(in)g([)p FB(A)1702 2721 y Fw(op)1780 2751 y FF(;)14 b Fv(2)p FL(].)60 b(Hence)35 b FF(a)g FL(is)g(in)f(the)i(lo)n(w)n(erset)c Fv(m)3035 2763 y Ft(A)3105 2751 y FL(\()p FB(W)23 b FL(\))36 b(i\013)f(there)g(exists)e(a)0 2851 y(lo)n(w)n(erset)25 b FF(W)40 b FL(in)26 b FB(W)51 b FL(suc)n(h)27 b(that)h FF(a)g FL(is)e(in)h FF(W)12 b FL(.)37 b(The)27 b(follo)n(wing)d(result) i(is)h(pro)n(v)n(ed)f(in)h(Section)f(2.5)h(of)h([)3165 2851 y SDict begin H.S end 3165 2851 a Black FL(MR)-9 b(W)p Black 3378 2794 a SDict begin H.R end 3378 2794 a 3378 2851 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.marmolejo+rosebrugh+wood) cvn H.B /ANN pdfmark end 3378 2851 a FL(]:)0 3017 y SDict begin H.S end 0 3017 a 0 3017 a SDict begin 12 H.A end 0 3017 a 0 3017 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.7) cvn /DEST pdfmark end 0 3017 a Black FM(Prop)s(osition)32 b(2.7.)p Black 42 w FC(The)g(2-functor)g FL(\()p FK(\000)p FL(\))1374 3029 y FJ(\005)1438 3017 y FL(:)27 b FI(Pre)f FK(\000)-14 b(!)26 b FI(Rel)p FL(\()p FI(Pre)p FL(\))32 b FC(exhibits)g FI(Rel)p FL(\()p FI(Pre)p FL(\))g FC(as)g(a)g(Kleisli)h (c)l(ate)l(gory)f(for)h(the)e(KZ)0 3116 y(do)l(ctrine)f FL(\()p Fv(L)p FF(;)14 b Fv(y)p FF(;)g Fv(m)p FL(\))p FC(.)0 3253 y SDict begin H.S end 0 3253 a 0 3253 a SDict begin 12 H.A end 0 3253 a 0 3253 a SDict begin [/View [/XYZ H.V]/Dest (subsection.2.3) cvn /DEST pdfmark end 0 3253 a 96 x Fs(2.C)112 b(Relations)38 b(as)g(spans)0 3502 y FL(Monotone)27 b(relations)d(are)j(going)e(to)j(b)r(e)g(exactly)e (certain)g(spans,)h(called)e FC(two-side)l(d)31 b(discr)l(ete)f(\014br) l(ations)35 b FL([)3409 3514 y SDict begin H.S end 3409 3514 a Black -12 x FL(S)3455 3514 y FE(4)p Black 3492 3445 a SDict begin H.R end 3492 3445 a 3492 3502 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.street:fibrations) cvn H.B /ANN pdfmark end 3492 3502 a FL(].)0 3668 y SDict begin H.S end 0 3668 a 0 3668 a SDict begin 12 H.A end 0 3668 a 0 3668 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.8) cvn /DEST pdfmark end 0 3668 a Black FM(De\014nition)c(2.8.)p Black 40 w FL(A)d FC(sp)l(an)34 b FL(\()p FF(d)996 3680 y FE(0)1034 3668 y FF(;)14 b FB(E)h FF(;)f(d)1213 3680 y FE(1)1250 3668 y FL(\))23 b(:)h FB(B)i FK(\000)-14 b(!)23 b FB(A)47 b FL(from)26 b FB(B)31 b FL(to)d FB(A)46 b FL(is)27 b(a)g(diagram)1922 3863 y FB(E)1751 3904 y Fz(d)1786 3912 y Fl(0)1773 3981 y Fy({)p Fx({)p FA(x)1804 3958 y(x)1834 3934 y(x)1865 3911 y(x)2088 3904 y Fz(d)2123 3912 y Fl(1)2134 3983 y Fy(#)p Fx(#)2101 3958 y FA(F)2071 3934 y(F)2040 3910 y(F)2009 3886 y(F)1662 4054 y FB(A)430 b(B)0 4232 y FL(of)28 b(monotone)d(maps.)36 b(The)28 b(preorder)d FB(E)43 b FL(is)27 b(called)e(the)j FC(vertex)37 b FL(of)28 b(the)g(span)f(\()p FF(d)2542 4244 y FE(0)2580 4232 y FF(;)14 b FB(E)h FF(;)f(d)2759 4244 y FE(1)2796 4232 y FL(\).)0 4398 y SDict begin H.S end 0 4398 a 0 4398 a SDict begin 12 H.A end 0 4398 a 0 4398 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.9) cvn /DEST pdfmark end 0 4398 a Black FM(Remark)36 b(2.9.)p Black 42 w FL(Giv)n(en)31 b(a)h(span)f(\()p FF(d)1152 4410 y FE(0)1190 4398 y FF(;)14 b FB(E)h FF(;)f(d)1369 4410 y FE(1)1406 4398 y FL(\))31 b(:)f FB(B)k FK(\000)-14 b(!)30 b FB(A)19 b FL(,)33 b(the)f(follo)n (wing)c(in)n(tuitiv)n(e)h(notation)h(migh)n(t)g(pro)n(v)n(e)h(useful:) 44 b(a)0 4498 y(t)n(ypical)25 b(elemen)n(t)h(of)h FB(E)43 b FL(will)25 b(b)r(e)j(denoted)g(b)n(y)f(a)g(wiggly)e(arro)n(w)1642 4701 y FF(d)1685 4713 y FE(0)1722 4701 y FL(\()p FF(e)p FL(\))1934 4655 y Fz(e)2050 4680 y Fy(/)p Fx(/)2009 4682 y Fk(/o)1950 4680 y(/o)1891 4679 y(/o)2075 4701 y FF(d)2118 4713 y FE(1)2155 4701 y FL(\()p FF(e)p FL(\))0 4900 y(and)i FF(d)204 4912 y FE(0)242 4900 y FL(\()p FF(e)p FL(\))h(will)d(b)r(e)j (the)g FC(domain)35 b FL(of)28 b FF(e)f FL(and)g FF(d)1452 4912 y FE(1)1490 4900 y FL(\()p FF(e)p FL(\))h(the)g FC(c)l(o)l(domain)35 b FL(of)28 b FF(e)p FL(.)p Black 1929 5400 a(5)p Black eop end end %%Page: 6 6 TeXDict begin HPSdict begin 6 5 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.6) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a SDict begin H.S end 0 83 a 0 83 a SDict begin 12 H.A end 0 83 a 0 83 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.10) cvn /DEST pdfmark end 0 83 a Black FM(De\014nition)38 b(2.10.)p Black 44 w FL(A)d(span)f(\()p FF(d)1068 95 y FE(0)1105 83 y FF(;)14 b FB(E)h FF(;)f(d)1284 95 y FE(1)1322 83 y FL(\))34 b(:)g FB(B)k FK(\000)-14 b(!)34 b FB(A)53 b FL(in)34 b FI(Pre)g FL(is)f(a)h FC(two-side)l(d)j(discr)l (ete)g(\014br)l(ation)k FL(\(w)n(e)34 b(will)d(sa)n(y)i(just)0 183 y FC(\014br)l(ation)39 b FL(in)31 b(what)h(follo)n(ws\),)f(if)h (the)g(follo)n(wing)c(three)k(conditions)e(are)h(satis\014ed.)50 b(F)-7 b(or)31 b(ev)n(ery)g(situation)f(b)r(elo)n(w)h(on)h(the)0 282 y(left,)27 b(there)h(is)e(a)h(unique)g(\014ll)f(in)h(on)g(the)h (righ)n(t,)e(denoted)i(b)n(y)f(\()p FF(d)2006 294 y FE(0)2044 282 y FL(\))2076 294 y FJ(\003)2114 282 y FL(\()p FF(e)2185 252 y FJ(0)2209 282 y FL(\),)h(resp)r(ectiv)n(ely)c(\()p FF(d)2819 294 y FE(1)2857 282 y FL(\))2889 294 y FJ(\003)2928 282 y FL(\()p FF(e)p FL(\):)1313 526 y FF(a)1334 737 y Fy(\017)p Fx(\017)p 1333 737 4 186 v 1301 824 a FF(a)1345 794 y FJ(0)1464 876 y Fz(e)1495 851 y Fq(0)1592 803 y Fy(/)p Fx(/)1552 804 y Fk(/o)1493 803 y(/o)1433 802 y(/o)1617 824 y FF(b)1653 794 y FJ(0)2236 526 y FF(a)2284 466 y FE(\()p Fz(d)2345 474 y Fl(0)2377 466 y FE(\))2403 474 y Fq(\003)2437 466 y FE(\()p Fz(e)2494 441 y Fq(0)2517 466 y FE(\))2515 505 y Fy(/)p Fx(/)2469 506 y Fk(/o)2410 505 y(/o)2351 504 y(/o)2258 750 y Fy(\017)p Fx(\017)p 2256 750 4 200 v 2540 526 a FF(b)2576 496 y FJ(0)p 2576 750 V 2560 750 V 2224 837 a FF(a)2268 807 y FJ(0)2387 890 y Fz(e)2418 865 y Fq(0)2515 817 y Fy(/)p Fx(/)2475 818 y Fk(/o)2416 817 y(/o)2357 815 y(/o)2540 837 y FF(b)2576 807 y FJ(0)1324 1104 y FF(a)1481 1058 y Fz(e)1604 1083 y Fy(/)p Fx(/)1558 1084 y Fk(/o)1498 1083 y(/o)1439 1082 y(/o)1629 1104 y FF(b)1647 1325 y Fy(\017)p Fx(\017)p 1645 1325 4 197 v 1617 1413 a FF(b)1653 1383 y FJ(0)2224 1104 y FF(a)2380 1058 y Fz(e)2504 1083 y Fy(/)p Fx(/)2457 1084 y Fk(/o)2398 1083 y(/o)2339 1082 y(/o)p 2253 1352 4 224 v 2236 1352 V 2529 1104 a FF(b)2546 1325 y Fy(\017)p Fx(\017)p 2545 1325 4 197 v 2224 1413 a FF(a)2278 1461 y FE(\()p Fz(d)2339 1469 y Fl(1)2371 1461 y FE(\))2397 1469 y Fq(\003)2431 1461 y FE(\()p Fz(e)p FE(\))2492 1392 y Fy(/)p Fx(/)2452 1393 y Fk(/o)2392 1392 y(/o)2333 1391 y(/o)2517 1413 y FF(b)2553 1383 y FJ(0)0 1615 y FL(Ev)n(ery)i(situation)f(on)j(the)g(left)f(can)g(b)r(e)h(written)f(as) g(depicted)g(on)g(the)h(righ)n(t:)1313 1816 y FF(a)1475 1770 y Fz(e)1604 1795 y Fy(/)p Fx(/)1552 1797 y Fk(/o)1493 1795 y(/o)1433 1794 y(/o)1334 2038 y Fy(\017)p Fx(\017)p 1333 2038 V 1629 1816 a FF(b)1647 2038 y Fy(\017)p Fx(\017)p 1645 2038 V 1301 2125 a FF(a)1345 2095 y FJ(0)1464 2177 y Fz(e)1495 2152 y Fq(0)1592 2104 y Fy(/)p Fx(/)1552 2106 y Fk(/o)1493 2104 y(/o)1433 2103 y(/o)1617 2125 y FF(b)1653 2095 y FJ(0)2236 1816 y FF(a)2398 1770 y Fz(e)2527 1795 y Fy(/)p Fx(/)2475 1797 y Fk(/o)2416 1795 y(/o)2357 1794 y(/o)p 2264 2064 4 224 v 2248 2064 V 2552 1816 a FF(b)2570 2038 y Fy(\017)p Fx(\017)p 2568 2038 4 197 v 2236 2125 a FF(a)2515 2104 y Fy(/)p Fx(/)2469 2106 y Fk(/o)2410 2104 y(/o)2351 2103 y(/o)2258 2349 y Fy(\017)p Fx(\017)p 2256 2349 4 200 v 2540 2125 a FF(b)2576 2095 y FJ(0)p 2576 2349 V 2560 2349 V 2224 2437 a FF(a)2268 2406 y FJ(0)2387 2489 y Fz(e)2418 2464 y Fq(0)2515 2416 y Fy(/)p Fx(/)2475 2417 y Fk(/o)2416 2416 y(/o)2357 2415 y(/o)2540 2437 y FF(b)2576 2406 y FJ(0)0 2666 y FM(Remark.)85 b FL(Fibrations)25 b(are)j(join)n(tly)f(mono.)38 b(In)29 b(particular,)d(if)i FB(B)s FF(;)14 b FB(A)48 b FL(are)27 b(discrete)g(then)j(\()p FF(d)3039 2678 y FE(0)3076 2666 y FF(;)14 b FB(E)h FF(;)f(d)3255 2678 y FE(1)3293 2666 y FL(\))25 b(:)g FB(B)j FK(\000)-14 b(!)25 b FB(A)47 b FL(is)27 b(a)0 2765 y(\014bration)f(i\013)h(it)g(is)g(a)g(join)n(tly) e(mono.)0 2930 y SDict begin H.S end 0 2930 a 0 2930 a SDict begin 12 H.A end 0 2930 a 0 2930 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.11) cvn /DEST pdfmark end 0 2930 a Black FM(De\014nition)31 b(2.11.)p Black 40 w FL(A)d FC(c)l(omma)i(obje)l(ct)36 b FL(of)28 b(monotone)e(maps)g FF(f)31 b FL(:)24 b FB(A)41 b FK(\000)-14 b(!)23 b FB(C)14 b FL(,)28 b FF(g)e FL(:)d FB(B)k FK(\000)-15 b(!)24 b FB(C)42 b FL(is)26 b(a)h(diagram)1722 3143 y FF(f)9 b(=g)1946 3086 y Fz(p)1980 3094 y Fl(1)2079 3122 y Fy(/)p Fx(/)p 1880 3123 200 4 v 1697 3288 a Fz(p)1731 3296 y Fl(0)1788 3379 y Fy(\017)p Fx(\017)p 1787 3379 4 191 v 1933 3296 a FJ(\045)2104 3143 y FB(B)2169 3288 y Fz(g)2144 3379 y Fy(\017)p Fx(\017)p 2142 3379 4 212 v 1746 3462 a FB(A)1951 3507 y Fz(f)2084 3441 y Fy(/)p Fx(/)p 1856 3443 228 4 v 2109 3462 a FB(C)0 3695 y FL(where)32 b(elemen)n(ts)e(of)i(the)g (preorder)f FF(f)9 b(=g)34 b FL(are)d(pairs)f(\()p FF(a;)14 b(b)p FL(\))32 b(with)g FF(f)9 b FL(\()p FF(a)p FL(\))31 b FK(\024)f FF(g)s FL(\()p FF(b)p FL(\))i(in)f FB(C)15 b FL(,)33 b(the)g(preorder)d(on)i FF(f)9 b(=g)34 b FL(is)d(de\014ned)0 3794 y(p)r(oin)n(t)n(wise)25 b(and)h FF(p)569 3806 y FE(0)633 3794 y FL(and)h FF(p)836 3806 y FE(1)900 3794 y FL(are)f(the)i(pro)5 b(jections.)34 b(The)27 b(whole)f(\\lax)f(comm)n (utativ)n(e)e(square")i(as)i(ab)r(o)n(v)n(e)e(will)f(b)r(e)k(called)c (a)0 3894 y FC(c)l(omma)30 b(squar)l(e)6 b FL(.)0 4059 y SDict begin H.S end 0 4059 a 0 4059 a SDict begin 12 H.A end 0 4059 a 0 4059 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.12) cvn /DEST pdfmark end 0 4059 a Black FM(Example)46 b(2.12.)p Black 47 w FL(Ev)n(ery)40 b(span)g(\()p FF(p)1189 4071 y FE(0)1226 4059 y FF(;)14 b(f)9 b(=g)s(;)14 b(p)1477 4071 y FE(1)1513 4059 y FL(\))46 b(:)f FB(A)64 b FK(\000)-14 b(!)45 b FB(B)g FL(arising)37 b(from)j(a)g(comma)f(ob)5 b(ject)40 b(of)h FF(f)54 b FL(:)46 b FB(A)64 b FK(\000)-15 b(!)46 b FB(C)14 b FL(,)0 4158 y FF(g)26 b FL(:)d FB(B)k FK(\000)-15 b(!)23 b FB(C)42 b FL(is)27 b(a)g(\014bration.)125 4358 y(A)e(monotone)e(relation)31 b FB(B)1083 4357 y FA(\025)p 990 4339 100 4 v 1064 4312 a Fz(R)1189 4337 y Fy(/)p Fx(/)p 1089 4339 V 1197 4358 a FB(A)52 b FL(induces)25 b(a)f(\014bration)g(\()p FF(d)2086 4370 y FE(0)2123 4358 y FF(;)14 b FB(E)h FF(;)f(d)2302 4370 y FE(1)2340 4358 y FL(\))23 b(:)g FB(B)k FK(\000)-14 b(!)23 b FB(A)44 b FL(with)24 b FB(E)38 b FL(=)23 b FK(f)p FL(\()p FF(a;)14 b(b)p FL(\))22 b FK(j)i FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))22 b(=)h(1)p FK(g)0 4458 y FL(ordered)30 b(b)n(y)i(\()p FF(a;)14 b(b)p FL(\))29 b FK(\024)h FL(\()p FF(a)805 4428 y FJ(0)828 4458 y FF(;)14 b(b)901 4428 y FJ(0)924 4458 y FL(\),)33 b(if)e FF(a)f FK(\024)f FF(a)1304 4428 y FJ(0)1359 4458 y FL(and)j FF(b)d FK(\024)g FF(b)1720 4428 y FJ(0)1743 4458 y FL(;)34 b(and)d(\()p FF(d)2040 4470 y FE(0)2078 4458 y FF(;)14 b FB(E)h FF(;)f(d)2257 4470 y FE(1)2294 4458 y FL(\))32 b(induces)f(the)h(relation)d FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))29 b(=)h(1)61 b FK(,)g(9)p FF(e)30 b FK(2)0 4557 y FB(E)f FF(:)14 b(d)156 4569 y FE(0)193 4557 y FL(\()p FF(e)p FL(\))24 b(=)e FF(a;)14 b(d)531 4569 y FE(1)568 4557 y FL(\()p FF(e)p FL(\))24 b(=)e FF(b)p FL(.)0 4722 y SDict begin H.S end 0 4722 a 0 4722 a SDict begin 12 H.A end 0 4722 a 0 4722 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.13) cvn /DEST pdfmark end 0 4722 a Black FM(Prop)s(osition)36 b(2.13.)p Black 43 w FC(Fibr)l(ations)f(in)g FI(Pre)g FC(c)l(orr)l(esp)l(ond)g (exactly)g(to)f(monotone)h(r)l(elations.)53 b(Mor)l(e)l(over,)38 b(if)d FL(\()p FF(d)3559 4734 y FE(0)3597 4722 y FF(;)14 b FB(E)h FF(;)f(d)3776 4734 y FE(1)3813 4722 y FL(\))32 b(:)0 4822 y FB(B)27 b FK(\000)-14 b(!)23 b FB(A)48 b FC(is)30 b(the)g(\014br)l(ation)g(c)l(orr)l(esp)l(onding)h(to)f(a)g(r)l (elation)39 b FF(R)23 b FL(:)g FB(B)2253 4821 y FA(\025)p 2159 4803 100 4 v 2359 4801 a Fy(/)p Fx(/)p 2259 4803 V 2367 4822 a FB(A)k FC(,)j(then)g FF(R)23 b FL(=)g(\()p FF(d)2950 4834 y FE(0)2988 4822 y FL(\))3020 4834 y FJ(\005)3077 4822 y FK(\001)18 b FL(\()p FF(d)3193 4834 y FE(1)3231 4822 y FL(\))3263 4791 y FJ(\005)3301 4822 y FC(.)p Black 0 4986 a(Pr)l(o)l(of.)p Black 43 w FL(This)27 b(is)f(seen)i(b)n(y)f (the)h(follo)n(wing)23 b FC(Gr)l(othendie)l(ck)32 b(c)l(onstruction)p FL(:)0 5035 y SDict begin H.S end 0 5035 a 0 5035 a SDict begin 12 H.A end 0 5035 a 0 5035 a SDict begin [/View [/XYZ H.V]/Dest (Item.7) cvn /DEST pdfmark end 0 5035 a Black 101 5151 a FL(1.)p Black 42 w(Giv)n(en)26 b(a)h(relation)e FF(R)f FL(:)f FB(A)1040 5121 y Fw(op)1136 5151 y FK(\002)c FB(B)26 b FK(\000)-14 b(!)23 b Fv(2)p FL(,)28 b(de\014ne)g(the)g(span)f (\()p FF(d)2227 5163 y FE(0)2265 5151 y FF(;)14 b FB(E)h FF(;)f(d)2444 5163 y FE(1)2481 5151 y FL(\))23 b(:)h FB(B)i FK(\000)-14 b(!)23 b FB(A)46 b FL(as)27 b(follo)n(ws:)p Black 1929 5400 a(6)p Black eop end end %%Page: 7 7 TeXDict begin HPSdict begin 7 6 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.7) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.8) cvn /DEST pdfmark end 0 0 a Black 243 83 a FL(\(a\))p Black 41 w(Ob)5 b(jects)22 b(of)g FB(E)38 b FL(are)21 b(pairs)g(\()p FF(a;)14 b(b)p FL(\),)23 b(where)f FF(a)g FL(and)g FF(b)h FL(are)e(ob)5 b(jects)22 b(of)g FB(A)41 b FL(and)22 b FB(B)s FL(,)j(resp)r(ectiv)n(ely)-7 b(,)20 b(with)i FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))23 b(=)f(1.)390 183 y(A)28 b(t)n(ypical)d(ob)5 b(ject)28 b(is)e(going)g(to)h(b)r(e)h (denoted)g(b)n(y)1981 391 y FF(a)2081 331 y FE(\()p Fz(a;b)p FE(\))2249 370 y Fy(/)p Fx(/)2208 371 y Fk(/o)2149 370 y(/o)2090 369 y(/o)2274 391 y FF(b)0 471 y SDict begin H.S end 0 471 a 0 471 a SDict begin 12 H.A end 0 471 a 0 471 a SDict begin [/View [/XYZ H.V]/Dest (Item.9) cvn /DEST pdfmark end 0 471 a Black 238 557 a FL(\(b\))p Black 42 w(The)37 b(preorder)e(relation)e(on)k FB(E)15 b FL(:)55 b(w)n(e)36 b(put)h(\()p FF(a;)14 b(b)p FL(\))38 b FK(\024)g FL(\()p FF(a)2180 527 y FJ(0)2203 557 y FF(;)14 b(b)2276 527 y FJ(0)2299 557 y FL(\),)40 b(if)c FF(a)i FK(\024)f FF(a)2707 527 y FJ(0)2730 557 y FL(,)j FF(b)d FK(\024)h FF(b)3005 527 y FJ(0)3065 557 y FL(in)d FB(A)19 b FL(,)39 b FB(B)s FL(,)h(resp)r(ectiv)n(ely)-7 b(.)390 656 y(Diagrammatical)o(l)o(y:)1969 809 y FF(a)2081 749 y FE(\()p Fz(a;b)p FE(\))2261 789 y Fy(/)p Fx(/)2208 790 y Fk(/o)2149 789 y(/o)2090 787 y(/o)1991 1031 y Fy(\017)p Fx(\017)p 1989 1031 4 197 v 2285 809 a FF(b)2303 1031 y Fy(\017)p Fx(\017)p 2302 1031 V 1958 1119 a FF(a)2002 1088 y FJ(0)2058 1171 y FE(\()p Fz(a)2120 1146 y Fq(0)2143 1171 y Fz(;b)2192 1146 y Fq(0)2214 1171 y FE(\))2249 1098 y Fy(/)p Fx(/)2208 1099 y Fk(/o)2149 1098 y(/o)2090 1097 y(/o)2274 1119 y FF(b)2310 1088 y FJ(0)390 1314 y FL(\(where)28 b(w)n(e)f(write,)f(e.g.,)i FF(a)22 b FK(\000)-14 b(!)23 b FF(a)1463 1284 y FJ(0)1514 1314 y FL(to)28 b(denote)f FF(a)c FK(\024)g FF(a)2082 1284 y FJ(0)2105 1314 y FL(\).)0 1346 y SDict begin H.S end 0 1346 a 0 1346 a SDict begin 12 H.A end 0 1346 a 0 1346 a SDict begin [/View [/XYZ H.V]/Dest (Item.10) cvn /DEST pdfmark end 0 1346 a Black 247 1436 a FL(\(c\))p Black 42 w(The)28 b(monotone)e(maps)g FF(d)1204 1448 y FE(0)1264 1436 y FL(:)d FB(E)38 b FK(\000)-14 b(!)23 b FB(A)46 b FL(and)28 b FF(d)1870 1448 y FE(1)1930 1436 y FL(:)23 b FB(E)39 b FK(\000)-15 b(!)23 b FB(B)32 b FL(are)26 b(then)i(the)g(ob)n(vious)d(domain)g(and)j(co)r(domain)390 1535 y(pro)5 b(jections.)208 1690 y(W)-7 b(e)28 b(v)n(erify)d(no)n(w)i (that)h(\()p FF(d)1009 1702 y FE(0)1047 1690 y FF(;)14 b FB(E)h FF(;)f(d)1226 1702 y FE(1)1263 1690 y FL(\))28 b(is)f(a)g(\014bration.)0 1755 y SDict begin H.S end 0 1755 a 0 1755 a SDict begin 12 H.A end 0 1755 a 0 1755 a SDict begin [/View [/XYZ H.V]/Dest (Item.11) cvn /DEST pdfmark end 0 1755 a Black 243 1845 a FL(\(a\))p Black 41 w(Supp)r(ose)1969 1945 y FF(a)1991 2156 y Fy(\017)p Fx(\017)p 1989 2156 4 186 v 1958 2243 a FF(a)2002 2213 y FJ(0)2058 2295 y FE(\()p Fz(a)2120 2270 y Fq(0)2143 2295 y Fz(;b)2192 2270 y Fq(0)2214 2295 y FE(\))2249 2222 y Fy(/)p Fx(/)2208 2223 y Fk(/o)2149 2222 y(/o)2090 2221 y(/o)2274 2243 y FF(b)2310 2213 y FJ(0)390 2434 y FL(is)g(giv)n(en.)35 b(W)-7 b(e)28 b(de\014ne)g(the)g(cartesian)d (lift)h(as)h(follo)n(ws:)1969 2647 y FF(a)2064 2586 y FE(\()p Fz(a;b)2175 2561 y Fq(0)2197 2586 y FE(\))2249 2626 y Fy(/)p Fx(/)2203 2627 y Fk(/o)2143 2626 y(/o)2084 2625 y(/o)1991 2871 y Fy(\017)p Fx(\017)p 1989 2871 4 200 v 2274 2647 a FF(b)2310 2616 y FJ(0)p 2310 2871 V 2293 2871 V 1958 2958 a FF(a)2002 2928 y FJ(0)2058 3010 y FE(\()p Fz(a)2120 2985 y Fq(0)2143 3010 y Fz(;b)2192 2985 y Fq(0)2214 3010 y FE(\))2249 2937 y Fy(/)p Fx(/)2208 2939 y Fk(/o)2149 2937 y(/o)2090 2936 y(/o)2274 2958 y FF(b)2310 2928 y FJ(0)390 3171 y FL(Here)g(w)n(e)h(ha)n(v)n(e)e(used) i(the)g(fact)f(that)h FF(R)h FL(is)d(monotone.)0 3182 y SDict begin H.S end 0 3182 a 0 3182 a SDict begin 12 H.A end 0 3182 a 0 3182 a SDict begin [/View [/XYZ H.V]/Dest (Item.12) cvn /DEST pdfmark end 0 3182 a Black 238 3293 a FL(\(b\))p Black 42 w(Giv)n(en)1969 3450 y FF(a)2075 3390 y FE(\()p Fz(a;b)p FE(\))2249 3429 y Fy(/)p Fx(/)2203 3431 y Fk(/o)2143 3429 y(/o)2084 3428 y(/o)2274 3450 y FF(b)2292 3672 y Fy(\017)p Fx(\017)p 2290 3672 4 197 v 2262 3759 a FF(b)2298 3729 y FJ(0)390 3888 y FL(and)i FF(g)d FL(:)e FF(b)g FK(\000)-14 b(!)23 b FF(b)915 3858 y FJ(0)938 3888 y FL(,)28 b(pro)r(ceed)f(analogously)c(to)k(the)h (ab)r(o)n(v)n(e:)36 b(de\014ne)27 b(the)h(unique)f(op)r(cartesian)e (lift)i(as)g(follo)n(ws)1969 4096 y FF(a)2075 4036 y FE(\()p Fz(a;b)p FE(\))2249 4076 y Fy(/)p Fx(/)2203 4077 y Fk(/o)2143 4076 y(/o)2084 4074 y(/o)p 1998 4345 4 224 v 1981 4345 V 2274 4096 a FF(b)2292 4318 y Fy(\017)p Fx(\017)p 2290 4318 4 197 v 1969 4405 a FF(a)2062 4458 y FE(\()p Fz(a;b)2173 4433 y Fq(0)2195 4458 y FE(\))2237 4385 y Fy(/)p Fx(/)2197 4386 y Fk(/o)2138 4385 y(/o)2078 4383 y(/o)2262 4405 y FF(b)2298 4375 y FJ(0)0 4552 y SDict begin H.S end 0 4552 a 0 4552 a SDict begin 12 H.A end 0 4552 a 0 4552 a SDict begin [/View [/XYZ H.V]/Dest (Item.13) cvn /DEST pdfmark end 0 4552 a Black 247 4634 a FL(\(c\))p Black 42 w(Supp)r(ose)h(w)n(e)f(are)g(giv)n(en)e(a)j (morphism)1969 4792 y FF(a)2081 4731 y FE(\()p Fz(a;b)p FE(\))2261 4771 y Fy(/)p Fx(/)2208 4772 y Fk(/o)2149 4771 y(/o)2090 4770 y(/o)1991 5013 y Fy(\017)p Fx(\017)p 1989 5013 4 197 v 2285 4792 a FF(b)2303 5013 y Fy(\017)p Fx(\017)p 2302 5013 V 1958 5101 a FF(a)2002 5071 y FJ(0)2058 5153 y FE(\()p Fz(a)2120 5128 y Fq(0)2143 5153 y Fz(;b)2192 5128 y Fq(0)2214 5153 y FE(\))2249 5080 y Fy(/)p Fx(/)2208 5081 y Fk(/o)2149 5080 y(/o)2090 5079 y(/o)2274 5101 y FF(b)2310 5071 y FJ(0)p Black 1929 5400 a FL(7)p Black eop end end %%Page: 8 8 TeXDict begin HPSdict begin 8 7 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.8) cvn /DEST pdfmark end -8 -8 a Black Black 390 83 a FL(in)27 b FB(E)15 b FL(.)37 b(Then)28 b(it)f(is)f(straigh)n (tforw)n(ard)e(to)j(see)h(that)g(it)f(is)f(equal)g(to)i(the)g(comp)r (osite)1969 296 y FF(a)2081 236 y FE(\()p Fz(a;b)p FE(\))2261 276 y Fy(/)p Fx(/)2208 277 y Fk(/o)2149 276 y(/o)2090 274 y(/o)p 1998 545 4 224 v 1981 545 V 2285 296 a FF(b)2303 518 y Fy(\017)p Fx(\017)p 2302 518 4 197 v 1969 605 a FF(a)2064 545 y FE(\()p Fz(a;b)2175 520 y Fq(0)2197 545 y FE(\))2249 585 y Fy(/)p Fx(/)2203 586 y Fk(/o)2143 585 y(/o)2084 583 y(/o)1991 830 y Fy(\017)p Fx(\017)p 1989 830 4 200 v 2274 605 a FF(b)2310 575 y FJ(0)p 2310 830 V 2293 830 V 1958 917 a FF(a)2002 887 y FJ(0)2058 969 y FE(\()p Fz(a)2120 944 y Fq(0)2143 969 y Fz(;b)2192 944 y Fq(0)2214 969 y FE(\))2249 896 y Fy(/)p Fx(/)2208 897 y Fk(/o)2149 896 y(/o)2090 895 y(/o)1850 813 y Fj(@A)1933 896 y Fy(/)p Fx(/)p 1933 898 1 4 v 1850 359 a Fj(GF)p 1848 813 4 455 v 1933 277 12 4 v 2274 917 a FF(b)2310 887 y FJ(0)2358 813 y Fj(B)o(C)2358 896 y Fy(o)p Fx(o)p 2358 898 1 4 v -537 x Fj(E)o(D)p 2439 813 4 455 v 2346 277 12 4 v 0 1052 a SDict begin H.S end 0 1052 a 0 1052 a SDict begin 12 H.A end 0 1052 a 0 1052 a SDict begin [/View [/XYZ H.V]/Dest (Item.14) cvn /DEST pdfmark end 0 1052 a Black 101 1151 a FL(2.)p Black 42 w(Giv)n(en)e(a)h (\014bration)f(\()p FF(d)929 1163 y FE(0)967 1151 y FF(;)14 b FB(E)h FF(;)f(d)1146 1163 y FE(1)1183 1151 y FL(\))23 b(:)h FB(B)i FK(\000)-14 b(!)23 b FB(A)c FL(,)28 b(consider)d(the)j (follo)n(wing)c(de\014nition)939 1311 y FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))23 b(=)f(1)83 b(i\013)f(there)28 b(is)e FF(e)i FL(in)e FB(E)43 b FL(with)27 b FF(d)2354 1323 y FE(0)2392 1311 y FL(\()p FF(e)p FL(\))c(=)g FF(a)k FL(and)h FF(d)2882 1323 y FE(1)2919 1311 y FL(\()p FF(e)p FL(\))23 b(=)g FF(b)208 1471 y FL(That)k(the)h(assignmen)n(t)d(\()p FF(a;)14 b(b)p FL(\))23 b FK(7!)g FF(R)q FL(\()p FF(a;)14 b(b)p FL(\))27 b(giv)n(es)f(a)h(monotone)f(map)1703 1631 y FF(R)d FL(:)g FB(A)1921 1597 y Fw(op)2017 1631 y FK(\002)18 b FB(B)27 b FK(\000)-14 b(!)23 b Fv(2)208 1791 y FL(is)h(tak)n(en)i (care)f(of)h(b)n(y)g(the)g(three)g(conditions)e(of)i(De\014nition)2120 1791 y SDict begin H.S end 2120 1791 a Black FL(2.10)p Black 2268 1737 a SDict begin H.R end 2268 1737 a 2268 1791 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.2.10) cvn H.B /ANN pdfmark end 2268 1791 a FL(.)36 b(In)27 b(other)e(w)n (ords,)g(w)n(e)h(ha)n(v)n(e)f(obtained)f(a)i(relation)208 1890 y(from)g FB(B)31 b FL(to)d FB(A)18 b FL(.)p 3839 2038 4 57 v 3843 1985 50 4 v 3843 2038 V 3893 2038 4 57 v 0 2200 a FM(Corollary)-8 b(.)153 b FL(If)39 b(\()p FF(d)734 2212 y FE(0)772 2200 y FF(;)14 b FB(E)h FF(;)f(d)951 2212 y FE(1)988 2200 y FL(\))43 b(:)f FB(B)k FK(\000)-14 b(!)42 b FB(A)58 b FL(is)37 b(the)j(\014bration)d(corresp)r(onding)45 b FF(R)23 b FL(:)h FB(B)3014 2199 y FA(\025)p 2921 2181 100 4 v 3120 2179 a Fy(/)p Fx(/)p 3020 2181 V 3128 2200 a FB(A)j FL(,)42 b(then)e FI(Rel)o FL(\()p FF(V)19 b FL(\))p FF(R)43 b FL(=)0 2299 y FI(Rel)o FL(\()p FF(V)20 b FL(\)\(\()p FF(d)349 2311 y FE(0)387 2299 y FL(\))419 2311 y FJ(\005)476 2299 y FK(\001)e FL(\()p FF(d)592 2311 y FE(1)630 2299 y FL(\))662 2269 y FJ(\005)700 2299 y FL(\))24 b(=)e(\()p FF(V)e(d)986 2311 y FE(0)1023 2299 y FL(\))1055 2311 y FJ(\005)1112 2299 y FK(\001)e FL(\()p FF(V)i(d)1296 2311 y FE(1)1333 2299 y FL(\))1365 2269 y FJ(\005)1404 2299 y FL(.)p Black 0 2461 a FC(Pr)l(o)l(of.)p Black 43 w FL(On)31 b(the)h(left)f(w)n(e)g(ha)n(v)n(e)f(that)i FI(Rel)p FL(\()p FF(V)19 b FL(\)\(\()p FF(d)1552 2473 y FE(0)1590 2461 y FL(\))1622 2473 y FJ(\005)1681 2461 y FK(\001)j FL(\()p FF(d)1801 2473 y FE(1)1838 2461 y FL(\))1870 2431 y FJ(\005)1909 2461 y FL(\)\()p FF(b;)14 b(a)p FL(\))29 b(=)g(1)i(i\013)g(there)h(is)e FF(w)i FK(2)e FB(E)46 b FL(suc)n(h)31 b(that)h FF(b)d FK(\024)g FF(d)3571 2473 y FE(0)3609 2461 y FL(\()p FF(w)r FL(\))j(and)0 2560 y FF(d)43 2572 y FE(1)80 2560 y FL(\()p FF(w)r FL(\))25 b FK(\024)d FF(a)p FL(.)37 b(On)27 b(the)g(righ)n(t)e(w)n(e)i(ha)n(v)n (e)f(that)h(\(\()p FF(V)19 b(d)1567 2572 y FE(0)1605 2560 y FL(\))1637 2572 y FJ(\005)1692 2560 y FK(\001)f FL(\()p FF(V)h(d)1875 2572 y FE(1)1912 2560 y FL(\))1944 2530 y FJ(\005)1983 2560 y FL(\)\()p FF(b;)14 b(a)p FL(\))23 b(=)g(1)j(i\013)h(there)f(is)g FF(w)g FK(2)d FB(E)42 b FL(suc)n(h)27 b(that)g FF(b)c FL(=)g FF(d)3576 2572 y FE(0)3613 2560 y FL(\()p FF(w)r FL(\))28 b(and)0 2660 y FF(d)43 2672 y FE(1)80 2660 y FL(\()p FF(w)r FL(\))d(=)d FF(a)p FL(.)37 b(Since)27 b(\()p FF(d)713 2672 y FE(0)751 2660 y FF(;)14 b FB(E)h FF(;)f(d)930 2672 y FE(1)967 2660 y FL(\))28 b(is)f(a)g(\014bration)f(the)i(t)n(w)n(o)e(conditions)g (are)g(equiv)-5 b(alen)n(t.)p 3839 2660 4 57 v 3843 2607 50 4 v 3843 2660 V 3893 2660 4 57 v 0 2821 a SDict begin H.S end 0 2821 a 0 2821 a SDict begin 12 H.A end 0 2821 a 0 2821 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.14) cvn /DEST pdfmark end 0 2821 a Black FM(Remark)26 b(2.14.)p Black 36 w FL(The)e(prop)r(osition)c(can)k(b)r(e)g(extended)f (to)h(an)n(y)e(category)g(enric)n(hed)g(in)h FI(Pre)p FL(.)36 b(The)23 b(details)f(are)g(as)h(follo)n(ws.)0 2921 y(A)33 b(span)f(\()p FF(d)369 2933 y FE(0)406 2921 y FF(;)14 b FB(E)h FF(;)f(d)585 2933 y FE(1)623 2921 y FL(\))31 b(:)g FB(B)k FK(\000)-15 b(!)31 b FB(A)51 b FL(in)32 b FI(Pre)h FL(is)e(a)h FC(two-side)l(d)j(discr)l(ete)g (\014br)l(ation)6 b FL(,)34 b(if)e(the)h(follo)n(wing)28 b(three)k(conditions)e(are)0 3021 y(satis\014ed:)0 3040 y SDict begin H.S end 0 3040 a 0 3040 a SDict begin 12 H.A end 0 3040 a 0 3040 a SDict begin [/View [/XYZ H.V]/Dest (Item.15) cvn /DEST pdfmark end 0 3040 a Black 101 3169 a FL(1.)p Black 42 w(F)-7 b(or)27 b(eac)n(h)f FF(m)d FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(E)15 b FL(,)28 b FF(a;)14 b(a)1205 3138 y FJ(0)1251 3169 y FL(:)23 b FB(K)49 b FK(\000)-14 b(!)23 b FB(A)18 b FL(,)28 b FF(b)23 b FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(B)31 b FL(and)c FF(\013)d FL(:)f FF(a)2536 3138 y FJ(0)2582 3169 y FK(\000)-14 b(!)23 b FF(a)28 b FL(suc)n(h)f(that)h(triangles) 1345 3349 y FB(K)1548 3303 y Fz(m)1683 3328 y Fy(/)p Fx(/)p 1472 3330 212 4 v 1511 3532 a Fz(a)1671 3575 y Fy(!)p Fx(!)1641 3547 y FA(B)1613 3522 y(B)1585 3497 y(B)1558 3473 y(B)1530 3448 y(B)1502 3423 y(B)1475 3398 y(B)1447 3374 y(B)1708 3349 y FB(E)1764 3498 y Fz(d)1799 3506 y Fl(0)1739 3573 y Fy(\017)p Fx(\017)p 1737 3573 4 200 v 2280 3349 a FB(K)2481 3303 y Fz(m)2614 3328 y Fy(/)p Fx(/)p 2407 3330 208 4 v 2450 3547 a Fz(b)2606 3577 y Fy(!)p Fx(!)2575 3549 y FA(B)2548 3524 y(B)2520 3499 y(B)2492 3474 y(B)2464 3449 y(B)2437 3424 y(B)2409 3399 y(B)2381 3374 y(B)2639 3349 y FB(E)2695 3498 y Fz(d)2730 3506 y Fl(1)2670 3573 y Fy(\017)p Fx(\017)p 2669 3573 4 200 v 1696 3656 a FB(A)868 b(B)208 3812 y FL(comm)n(ute,)25 b(there)i(is)g(a)g(unique)43 b(\026)-58 b FF(m)23 b FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(E)42 b FL(and)28 b(a)f(unique)g FF(d)2280 3781 y FJ(\003)2280 3832 y FE(0)2318 3812 y FL(\()p FF(\013)p FL(\))d(:)39 b(\026)-58 b FF(m)23 b FK(\000)-14 b(!)23 b FF(m)28 b FL(suc)n(h)f(that)1345 4005 y FB(K)1561 3959 y FE(\026)-46 b Fz(m)1683 3984 y Fy(/)p Fx(/)p 1472 3986 212 4 v 1490 4211 a Fz(a)1526 4186 y Fq(0)1671 4231 y Fy(!)p Fx(!)1641 4203 y FA(B)1613 4178 y(B)1585 4153 y(B)1558 4129 y(B)1530 4104 y(B)1502 4079 y(B)1475 4054 y(B)1447 4030 y(B)1708 4005 y FB(E)1764 4154 y Fz(d)1799 4162 y Fl(0)1739 4229 y Fy(\017)p Fx(\017)p 1737 4229 4 200 v 2280 4005 a FB(K)2494 3959 y FE(\026)g Fz(m)2614 3984 y Fy(/)p Fx(/)p 2407 3986 208 4 v 2450 4203 a Fz(b)2606 4233 y Fy(!)p Fx(!)2575 4205 y FA(B)2548 4180 y(B)2520 4155 y(B)2492 4130 y(B)2464 4105 y(B)2437 4080 y(B)2409 4055 y(B)2381 4030 y(B)2639 4005 y FB(E)2695 4154 y Fz(d)2730 4162 y Fl(1)2670 4229 y Fy(\017)p Fx(\017)p 2669 4229 4 200 v 1696 4312 a FB(A)868 b(B)208 4463 y FL(and)1180 4637 y FB(K)1390 4544 y FE(\026)-46 b Fz(m)1506 4569 y Fy(/)p Fx(/)p 1307 4571 200 4 v 1377 4712 a Fz(m)1506 4662 y Fy(/)p Fx(/)p 1307 4664 V 1308 4630 a FJ(#)p Fz(d)1377 4605 y Fq(\003)1377 4646 y Fl(0)1411 4630 y FE(\()p Fz(\013)p FE(\))1531 4637 y FB(E)1684 4583 y Fz(d)1719 4591 y Fl(0)1817 4616 y Fy(/)p Fx(/)p 1618 4617 V 1842 4637 a FB(A)268 b FL(=)249 b FB(K)2688 4544 y Fz(a)2724 4519 y Fq(0)2817 4569 y Fy(/)p Fx(/)p 2617 4571 V 2699 4712 a Fz(a)2817 4662 y Fy(/)p Fx(/)p 2617 4664 V 2678 4631 a FJ(#)p Fz(\013)2842 4637 y FB(A)1180 4944 y(K)1390 4852 y FE(\026)-46 b Fz(m)1506 4876 y Fy(/)p Fx(/)p 1307 4878 V 1377 5019 a Fz(m)1506 4969 y Fy(/)p Fx(/)p 1307 4971 V 1308 4937 a FJ(#)p Fz(d)1377 4912 y Fq(\003)1377 4953 y Fl(0)1411 4937 y FE(\()p Fz(\013)p FE(\))1531 4944 y FB(E)1686 4890 y Fz(d)1721 4898 y Fl(1)1821 4923 y Fy(/)p Fx(/)p 1618 4925 203 4 v 1846 4944 a FB(B)256 b FL(=)249 b FB(K)2704 4898 y Fz(b)2820 4923 y Fy(/)p Fx(/)p 2617 4925 V 2845 4944 a FB(B)208 5151 y FL(comm)n(ute.)34 b(The)28 b(2-cell)d FF(d)1028 5121 y FJ(\003)1028 5172 y FE(0)1066 5151 y FL(\()p FF(\013)p FL(\))k(is)d(called)f(the)j FC(c)l(artesian)j(lift)36 b FL(of)28 b FF(\013)p FL(.)p Black 1929 5400 a(8)p Black eop end end %%Page: 9 9 TeXDict begin HPSdict begin 9 8 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.9) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.16) cvn /DEST pdfmark end 0 0 a Black 101 83 a FL(2.)p Black 42 w(F)-7 b(or)27 b(eac)n(h)f FF(m)d FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(E)15 b FL(,)28 b FF(a)23 b FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(A)18 b FL(,)28 b FF(b;)14 b(b)1720 53 y FJ(0)1766 83 y FL(:)23 b FB(K)49 b FK(\000)-15 b(!)23 b FB(B)32 b FL(and)27 b FF(\014)h FL(:)23 b FF(b)f FK(\000)-14 b(!)23 b FF(b)2733 53 y FJ(0)2784 83 y FL(suc)n(h)k(that)h(triangles)1345 278 y FB(K)1548 232 y Fz(m)1683 257 y Fy(/)p Fx(/)p 1472 259 212 4 v 1511 461 a Fz(a)1671 504 y Fy(!)p Fx(!)1641 476 y FA(B)1613 451 y(B)1585 427 y(B)1558 402 y(B)1530 377 y(B)1502 352 y(B)1475 328 y(B)1447 303 y(B)1708 278 y FB(E)1764 427 y Fz(d)1799 435 y Fl(0)1739 502 y Fy(\017)p Fx(\017)p 1737 502 4 200 v 2280 278 a FB(K)2481 232 y Fz(m)2614 257 y Fy(/)p Fx(/)p 2407 259 208 4 v 2450 476 a Fz(b)2606 506 y Fy(!)p Fx(!)2575 478 y FA(B)2548 453 y(B)2520 428 y(B)2492 403 y(B)2464 378 y(B)2437 353 y(B)2409 328 y(B)2381 303 y(B)2639 278 y FB(E)2695 427 y Fz(d)2730 435 y Fl(1)2670 502 y Fy(\017)p Fx(\017)p 2669 502 4 200 v 1696 585 a FB(A)868 b(B)208 756 y FL(comm)n(ute,)25 b(there)i(is)g(a)g(unique)43 b(\026)-58 b FF(m)23 b FL(:)g FB(K)49 b FK(\000)-14 b(!)23 b FB(E)42 b FL(and)28 b(a)f(unique)g FF(d)2280 725 y FJ(\003)2280 776 y FE(1)2318 756 y FL(\()p FF(\014)t FL(\))d(:)f FF(m)g FK(\))39 b FL(\026)-58 b FF(m)28 b FL(suc)n(h)f(that)1345 963 y FB(K)1561 918 y FE(\026)-46 b Fz(m)1683 943 y Fy(/)p Fx(/)p 1472 944 212 4 v 1511 1146 a Fz(a)1671 1189 y Fy(!)p Fx(!)1641 1162 y FA(B)1613 1137 y(B)1585 1112 y(B)1558 1087 y(B)1530 1063 y(B)1502 1038 y(B)1475 1013 y(B)1447 988 y(B)1708 963 y FB(E)1764 1112 y Fz(d)1799 1120 y Fl(0)1739 1188 y Fy(\017)p Fx(\017)p 1737 1188 4 200 v 2280 963 a FB(K)2494 918 y FE(\026)g Fz(m)2614 943 y Fy(/)p Fx(/)p 2407 944 208 4 v 2429 1169 a Fz(b)2458 1144 y Fq(0)2606 1192 y Fy(!)p Fx(!)2575 1164 y FA(B)2548 1139 y(B)2520 1114 y(B)2492 1089 y(B)2464 1064 y(B)2437 1039 y(B)2409 1013 y(B)2381 988 y(B)2639 963 y FB(E)2695 1112 y Fz(d)2730 1120 y Fl(1)2670 1188 y Fy(\017)p Fx(\017)p 2669 1188 4 200 v 1696 1271 a FB(A)868 b(B)208 1436 y FL(and)1180 1587 y FB(K)1377 1495 y Fz(m)1506 1520 y Fy(/)p Fx(/)p 1307 1521 200 4 v 1390 1671 a FE(\026)-46 b Fz(m)1506 1612 y Fy(/)p Fx(/)p 1307 1614 V 1309 1580 a FJ(#)p Fz(d)1378 1555 y Fq(\003)1378 1596 y Fl(1)1412 1580 y FE(\()p Fz(\014)s FE(\))1531 1587 y FB(E)1684 1533 y Fz(d)1719 1541 y Fl(0)1817 1566 y Fy(/)p Fx(/)p 1618 1568 V 1842 1587 a FB(A)268 b FL(=)249 b FB(K)2699 1541 y Fz(a)2817 1566 y Fy(/)p Fx(/)p 2617 1568 V 2842 1587 a FB(A)1180 1894 y(K)1377 1802 y Fz(m)1506 1827 y Fy(/)p Fx(/)p 1307 1828 V 1390 1978 a FE(\026)-46 b Fz(m)1506 1920 y Fy(/)p Fx(/)p 1307 1921 V 1309 1887 a FJ(#)p Fz(d)1378 1862 y Fq(\003)1378 1904 y Fl(1)1412 1887 y FE(\()p Fz(\014)s FE(\))1531 1894 y FB(E)1686 1840 y Fz(d)1721 1848 y Fl(1)1821 1873 y Fy(/)p Fx(/)p 1618 1875 203 4 v 1846 1894 a FB(B)256 b FL(=)249 b FB(K)2704 1802 y Fz(b)2820 1827 y Fy(/)p Fx(/)p 2617 1828 V 2693 1993 a Fz(b)2722 1968 y Fq(0)2820 1920 y Fy(/)p Fx(/)p 2617 1921 V 2681 1888 a FJ(#)p Fz(\014)2845 1894 y FB(B)208 2133 y FL(comm)n(ute.)34 b(The)28 b(2-cell)d FF(d)1028 2103 y FJ(\003)1028 2154 y FE(1)1066 2133 y FL(\()p FF(\014)t FL(\))k(is)d(called)f(the)j FC(op)l(c)l(artesian)j (lift)37 b FL(of)27 b FF(\014)t FL(.)0 2185 y SDict begin H.S end 0 2185 a 0 2185 a SDict begin 12 H.A end 0 2185 a 0 2185 a SDict begin [/View [/XYZ H.V]/Dest (Item.17) cvn /DEST pdfmark end 0 2185 a Black 101 2296 a FL(3.)p Black 42 w(Giv)n(en)e(an)n(y)h FF(\033)g FL(:)d FF(m)g FK(\))g FF(m)997 2266 y FJ(0)1043 2296 y FL(:)h FF(K)k FK(\000)-14 b(!)23 b FF(E)5 b FL(,)27 b(then)g(the)g(comp)r (osite)d FF(d)2224 2266 y FJ(\003)2224 2317 y FE(0)2262 2296 y FL(\()p FF(d)2337 2308 y FE(0)2375 2296 y FF(\033)s FL(\))17 b FK(\001)f FF(d)2556 2266 y FJ(\003)2556 2317 y FE(1)2594 2296 y FL(\()p FF(d)2669 2308 y FE(1)2707 2296 y FF(\033)s FL(\))27 b(is)f(de\014ned)h(and)f(it)g(is)f(equal)g (to)i FF(\033)s FL(.)0 2455 y(The)d(easiest)d(w)n(a)n(y)i(of)g (treating)f(\014brations)f(abstractly)h(is)g(that)i(they)g(are)e FC(algebr)l(as)32 b FL(for)23 b(t)n(w)n(o)f(\(2-\)monads)g(sim)n (ultaneously:)0 2555 y(they)28 b(are)e FC(two-side)l(d)31 b(mo)l(dules)k FL(in)27 b(a)g(certain)f(precise)g(sense.)36 b(See)28 b([)2141 2567 y SDict begin H.S end 2141 2567 a Black -12 x FL(S)2187 2567 y FE(2)p Black 2224 2498 a SDict begin H.R end 2224 2498 a 2224 2555 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.street1) cvn H.B /ANN pdfmark end 2224 2555 a FL(])g(and)g([)2460 2567 y SDict begin H.S end 2460 2567 a Black -12 x FL(S)2506 2567 y FE(4)p Black 2543 2498 a SDict begin H.R end 2543 2498 a 2543 2555 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.street:fibrations) cvn H.B /ANN pdfmark end 2543 2555 a FL(].)0 2727 y SDict begin H.S end 0 2727 a 0 2727 a SDict begin 12 H.A end 0 2727 a 0 2727 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.15) cvn /DEST pdfmark end 0 2727 a Black FM(Example)20 b(2.15.)p Black 31 w FL(Supp)r(ose)e(that)h FF(f)32 b FL(:)23 b FB(A)42 b FK(\000)-15 b(!)23 b FB(B)g FL(is)17 b(monotone.)32 b(Recall)16 b(the)j(relations)40 b FF(f)2837 2739 y FJ(\005)2898 2727 y FL(:)23 b FB(A)3110 2726 y FA(\025)p 3054 2708 63 4 v 3179 2706 a Fy(/)p Fx(/)p 3117 2708 V 3204 2727 a FB(B)47 b FL(and)c FF(f)3553 2697 y FJ(\005)3614 2727 y FL(:)23 b FB(B)3820 2726 y FA(\025)p 3764 2708 V 3888 2706 a Fy(/)p Fx(/)p 3826 2708 V 3913 2727 a FB(A)44 b FF(:)0 2827 y FL(Their)26 b(corresp)r(onding)f(\014brations)h(are)g(the)i(spans)1371 3013 y FC(id)1447 3025 y Ft(B)1512 3013 y FF(=f)1253 3058 y Fz(p)1287 3066 y Fl(0)1221 3156 y Fy(y)p Fx(y)p FA(s)1252 3138 y(s)1283 3119 y(s)1313 3100 y(s)1344 3081 y(s)1656 3058 y Fz(p)1690 3066 y Fl(1)1752 3155 y Fy(\045)p Fx(\045)1717 3133 y FA(K)1687 3115 y(K)1656 3096 y(K)1626 3077 y(K)1596 3059 y(K)2297 3013 y FF(f)9 b(=)p FC(id)2465 3025 y Ft(B)2178 3058 y Fz(p)2212 3066 y Fl(0)2148 3155 y Fy(y)p Fx(y)p FA(s)2178 3137 y(s)2208 3118 y(s)2239 3099 y(s)2269 3081 y(s)2581 3058 y Fz(p)2615 3066 y Fl(1)2679 3156 y Fy(\045)p Fx(\045)2643 3135 y FA(K)2613 3116 y(K)2582 3097 y(K)2551 3078 y(K)2521 3059 y(K)1118 3217 y FB(B)584 b(A)193 b(A)599 b(B)0 3382 y FL(arising)24 b(from)i(the)i(resp)r(ectiv) n(e)e(comma)f(squares.)0 3542 y SDict begin H.S end 0 3542 a 0 3542 a SDict begin 12 H.A end 0 3542 a 0 3542 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.16) cvn /DEST pdfmark end 0 3542 a Black FM(Example)k(2.16.)p Black 39 w FL(The)e(relation)d(\()p Fv(y)1175 3554 y Ft(A)1246 3542 y FL(\))1278 3512 y FJ(\005)1343 3542 y FL(from)h Fv(L)p FB(A)46 b FL(to)27 b FB(A)45 b FL(will)24 b(b)r(e)j(called)e (the)i FC(elementho)l(o)l(d)37 b FL(relation)24 b(and)i(denoted)h(b)n (y)0 3642 y FK(2)55 3654 y Ft(A)125 3642 y FL(,)h(since)e(\()p Fv(y)450 3654 y Ft(A)521 3642 y FL(\))553 3611 y FJ(\005)591 3642 y FL(\()p FF(a;)14 b(A)p FL(\))24 b(=)e Fv(L)p FB(A)d FL(\()p Fv(y)1117 3654 y Ft(A)1187 3642 y FF(a;)14 b(A)p FL(\))23 b(=)g FF(A)p FL(\()p FF(a)p FL(\))28 b(holds)f(b)n(y)g(the)h (Y)-7 b(oneda)27 b(Lemma.)0 3777 y SDict begin H.S end 0 3777 a 0 3777 a SDict begin 12 H.A end 0 3777 a 0 3777 a SDict begin [/View [/XYZ H.V]/Dest (subsection.2.4) cvn /DEST pdfmark end 0 3777 a 96 x Fs(2.D)112 b(Comp)s(osition)39 b(of)e(\014brations)0 4026 y FL(Supp)r(ose)c(that)h(w)n(e)e(ha)n(v)n(e) g(t)n(w)n(o)h(\014brations)e(as)h(on)h(the)h(left)f(b)r(elo)n(w.)52 b(W)-7 b(e)33 b(w)n(an)n(t)g(to)g(form)f(their)g(comp)r(osite)f FB(E)37 b FK(\012)21 b FB(F)45 b FC(as)36 b(a)0 4125 y(\014br)l(ation)6 b FL(.)980 4225 y FB(E)799 4313 y Fz(d)834 4288 y Fo(E)834 4329 y Fl(0)845 4416 y Fy(\002)p Fx(\002)p FA(\006)866 4389 y(\006)886 4363 y(\006)907 4336 y(\006)928 4309 y(\006)949 4283 y(\006)1146 4312 y Fz(d)1181 4287 y Fo(F)1181 4328 y Fl(1)1181 4416 y Fy(\034)p Fx(\034)1155 4384 y FA(9)1133 4357 y(9)1112 4330 y(9)1090 4304 y(9)1069 4277 y(9)1047 4250 y(9)1648 4225 y FB(F)1457 4309 y Fz(d)1492 4284 y Fo(F)1492 4326 y Fl(0)1511 4416 y Fy(\001)p Fx(\001)p FA(\004)1534 4389 y(\004)1557 4362 y(\004)1580 4335 y(\004)1602 4309 y(\004)1625 4282 y(\004)1833 4308 y Fz(d)1868 4283 y Fo(F)1868 4325 y Fl(1)1872 4416 y Fy(\035)p Fx(\035)1845 4384 y FA(:)1822 4357 y(:)1799 4331 y(:)1776 4304 y(:)1753 4277 y(:)1730 4250 y(:)761 4499 y FB(C)375 b(B)153 b(B)389 b(A)2655 4225 y(E)33 b FK(\012)18 b FB(F)2433 4300 y Fz(d)2468 4273 y Fo(E)7 b Fq(\012)p Fo(F)2468 4318 y Fl(0)2530 4428 y Fy(})p Fx(})p FA(|)2557 4405 y(|)2583 4381 y(|)2610 4357 y(|)2637 4333 y(|)2663 4309 y(|)2690 4285 y(|)2948 4300 y Fz(d)2983 4273 y Fo(E)g Fq(\012)p Fo(F)2983 4318 y Fl(1)3028 4423 y Fy(!)p Fx(!)2997 4395 y FA(C)2971 4372 y(C)2945 4349 y(C)2918 4326 y(C)2892 4303 y(C)2866 4280 y(C)2839 4257 y(C)2436 4503 y FB(C)562 b(A)0 4638 y FL(The)27 b(idea)f(is)f(similar)e(to)j(the)i(ordinary)c(relations:)33 b(the)27 b(comp)r(osite)e(is)h(going)f(to)h(b)r(e)i(a)e(quotien)n(t)g (of)h(a)f(pullbac)n(k)f(of)i(spans,)0 4738 y(this)g(time)f(the)i (quotien)n(t)e(will)f(b)r(e)j(tak)n(en)f(b)n(y)h(a)f(map)f(that)i(is)f (surjectiv)n(e)f(on)h(ob)5 b(jects,)27 b(hence)h FC(absolutely)j(dense) 6 b FL(.)0 4898 y SDict begin H.S end 0 4898 a 0 4898 a SDict begin 12 H.A end 0 4898 a 0 4898 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.17) cvn /DEST pdfmark end 0 4898 a Black FM(Remark)31 b(2.17.)p Black 40 w FL(A)d(monotone)d(map) i FF(e)c FL(:)g FB(A)41 b FK(\000)-14 b(!)23 b FB(B)32 b FL(is)26 b(called)f FC(absolutely)31 b(dense)k FL(\(see)27 b([)2859 4898 y SDict begin H.S end 2859 4898 a Black FL(ABSV)p Black 3089 4841 a SDict begin H.R end 3089 4841 a 3089 4898 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.absv) cvn H.B /ANN pdfmark end 3089 4898 a FL(])g(and)h([)3324 4898 y SDict begin H.S end 3324 4898 a Black FL(BV)p Black 3445 4841 a SDict begin H.R end 3445 4841 a 3445 4898 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.bv) cvn H.B /ANN pdfmark end 3445 4898 a FL(]\))g(i\013)1337 5089 y FB(B)s FL(\()p FF(b;)14 b(b)1556 5054 y FJ(0)1579 5089 y FL(\))23 b(=)1722 5010 y Fu(_)1750 5184 y Fz(a)1828 5089 y FB(B)s FL(\()p FF(b;)14 b(ea)p FL(\))19 b FK(^)g FB(B)s FL(\()p FF(ea;)14 b(b)2485 5054 y FJ(0)2508 5089 y FL(\))p FF(;)p Black 1929 5400 a FL(9)p Black eop end end %%Page: 10 10 TeXDict begin HPSdict begin 10 9 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.10) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a FL(that)26 b(is,)g FF(e)f FL(is)g(absolutely)e(dense)j(i\013)g FF(e)1185 95 y FJ(\005)1238 83 y FK(\001)15 b FF(e)1315 53 y FJ(\005)1376 83 y FL(=)22 b FC(id)10 b FL(.)36 b(Clearly)-7 b(,)24 b(ev)n(ery)g(monotone)h(map)f(surjectiv)n(e)h(on)h(ob)5 b(jects)25 b(is)g(absolutely)0 183 y(dense.)36 b(The)24 b(con)n(v)n(erse)f(is)g(true)i(if)f FB(B)k FL(is)c(a)g(p)r(oset.)36 b(If)25 b FB(B)j FL(is)c(a)g(preorder,)g(then)h FF(e)f FL(is)g(absolutely)d(dense)k(when)g(eac)n(h)e(strongly)0 282 y(connected)k(comp)r(onen)n(t)g(of)g FB(B)32 b FL(con)n(tains)25 b(at)j(least)e(one)h(elemen)n(t)f(in)h(the)h(image)d(of)i FF(e)p FL(.)125 427 y(In)g(de\014ning)g(the)h(comp)r(osition)c(of)j (\014brations)f(w)n(e)h(pro)r(ceed)g(as)g(follo)n(ws:)34 b(construct)27 b(the)h(pullbac)n(k)1632 615 y FB(E)34 b FK(\016)18 b FB(F)1952 558 y Fz(q)1982 566 y Fl(1)2083 595 y Fy(/)p Fx(/)p 1883 596 200 4 v 1658 755 a Fz(q)1688 763 y Fl(0)1745 840 y Fy(\017)p Fx(\017)p 1744 840 4 200 v 2107 615 a FB(F)2175 767 y Fz(d)2210 742 y Fo(F)2210 784 y Fl(0)2150 840 y Fy(\017)p Fx(\017)p 2149 840 V 1714 923 a FB(E)1904 981 y Fz(d)1939 956 y Fo(E)1939 997 y Fl(1)2086 902 y Fy(/)p Fx(/)p 1801 903 285 4 v 2111 923 a FB(B)0 1145 y FL(and)27 b(de\014ne)h FB(E)34 b FK(\012)18 b FB(F)39 b FL(to)28 b(b)r(e)g(the)g(follo)n(wing)23 b(preorder:)0 1179 y SDict begin H.S end 0 1179 a 0 1179 a SDict begin 12 H.A end 0 1179 a 0 1179 a SDict begin [/View [/XYZ H.V]/Dest (Item.18) cvn /DEST pdfmark end 0 1179 a Black 101 1291 a FL(1.)p Black 42 w(Ob)5 b(jects)20 b(are)g(wiggly)e(arro)n(ws)h(of)i(the)h(form)28 b FF(c)1820 1270 y Fy(/)p Fx(/)1780 1271 y Fk(/o)1720 1270 y(/o)1661 1269 y(/o)1828 1291 y FF(a)i FL(suc)n(h)21 b(that)g(there)g(exists)f FF(b)i FK(2)i FB(B)h FL(with)20 b(\()8 b FF(c)3388 1270 y Fy(/)p Fx(/)3348 1271 y Fk(/o)3289 1270 y(/o)3229 1269 y(/o)3396 1291 y FF(b)g(;)23 b(b)3729 1270 y Fy(/)p Fx(/)3688 1271 y Fk(/o)3629 1270 y(/o)3570 1269 y(/o)3737 1291 y FF(a)8 b FL(\))24 b FK(2)208 1390 y FB(E)33 b FK(\016)18 b FB(F)11 b FF(:)0 1418 y SDict begin H.S end 0 1418 a 0 1418 a SDict begin 12 H.A end 0 1418 a 0 1418 a SDict begin [/View [/XYZ H.V]/Dest (Item.19) cvn /DEST pdfmark end 0 1418 a Black 101 1546 a FL(2.)p Black 42 w(Put)35 b FF(c)622 1525 y Fy(/)p Fx(/)581 1526 y Fk(/o)522 1525 y(/o)463 1524 y(/o)630 1546 y FF(a)h FL(to)28 b(b)r(e)g(less)e(or)g (equal)g(to)36 b FF(c)1544 1516 y FJ(0)1775 1525 y Fy(/)p Fx(/)1735 1526 y Fk(/o)1675 1525 y(/o)1616 1524 y(/o)1783 1546 y FF(a)1827 1516 y FJ(0)1886 1546 y FL(i\013)28 b FF(c)23 b FK(\024)f FF(c)2168 1516 y FJ(0)2219 1546 y FL(and)28 b FF(a)23 b FK(\024)f FF(a)2579 1516 y FJ(0)2602 1546 y FL(.)0 1691 y(De\014ne)k(a)e(monotone)f(map)h FF(w)i FL(:)d FB(E)28 b FK(\016)13 b FB(F)35 b FK(\000)-15 b(!)23 b FB(E)29 b FK(\012)13 b FB(F)36 b FL(in)24 b(the)i(ob)n(vious)c (w)n(a)n(y)i(and)h(observ)n(e)e(that)i(it)g(is)f(surjectiv)n(e)f(on)i (ob)5 b(jects)0 1790 y(and,)27 b(hence,)h(absolutely)d(dense.)125 1890 y(W)-7 b(e)32 b(equip)e(no)n(w)h FB(E)36 b FK(\012)21 b FB(F)43 b FL(with)31 b(the)h(ob)n(vious)e(pro)5 b(jections)29 b FF(d)2081 1854 y Ft(E)11 b FJ(\012)p Ft(F)2081 1912 y FE(0)2281 1890 y FL(:)30 b FB(E)36 b FK(\012)21 b FB(F)41 b FK(\000)-14 b(!)29 b FB(C)46 b FL(and)32 b FF(d)3091 1854 y Ft(E)10 b FJ(\012)p Ft(F)3091 1912 y FE(1)3291 1890 y FL(:)30 b FB(E)36 b FK(\012)20 b FB(F)42 b FK(\000)-14 b(!)29 b FB(A)19 b FL(.)0 1990 y(Then)28 b(the)g(follo)n(wing)23 b(result)k(is)f(immediate.)0 2135 y SDict begin H.S end 0 2135 a 0 2135 a SDict begin 12 H.A end 0 2135 a 0 2135 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2.18) cvn /DEST pdfmark end 0 2135 a Black FM(Lemma)k(2.18.)p Black 39 w FC(The)h(sp)l(an)f FL(\()p FF(d)1012 2099 y Ft(E)11 b FJ(\012)p Ft(F)1012 2157 y FE(0)1183 2135 y FF(;)j FB(E)33 b FK(\012)18 b FB(F)11 b FF(;)j(d)1548 2099 y Ft(E)d FJ(\012)p Ft(F)1548 2157 y FE(1)1719 2135 y FL(\))23 b(:)g FB(A)42 b FK(\000)-14 b(!)23 b FB(C)44 b FC(is)30 b(a)g(\014br)l(ation.)125 2280 y FL(T)-7 b(o)27 b(summarize,)d(w)n(e)j (ha)n(v)n(e)0 2419 y FM(Prop)s(osition.)72 b FL(Let)21 b FF(S;)14 b(R)22 b FL(b)r(e)f(monotone)e(relations)f(with)i(asso)r (ciated)e(\014brations)h FB(E)c FF(;)f FB(F)d FL(.)35 b(Then)21 b(the)h(relation)17 b(asso)r(ciated)0 2518 y(with)27 b FB(E)34 b FK(\012)18 b FB(F)39 b FL(is)26 b FF(S)e FK(\001)18 b FF(R)q FL(,)28 b(that)f(is,)g(w)n(e)g(can)g (write)g FB(E)1615 2488 y Fz(S)s FJ(\001)p Fz(R)1756 2518 y FL(=)c FB(E)1906 2488 y Fz(S)1972 2518 y FK(\012)18 b FB(E)2117 2488 y Fz(R)2172 2518 y FL(.)0 2655 y SDict begin H.S end 0 2655 a 0 2655 a SDict begin 12 H.A end 0 2655 a 0 2655 a SDict begin [/View [/XYZ H.V]/Dest (section.3) cvn /DEST pdfmark end 0 2655 a 133 x FN(3)135 b(Exact)45 b(squares)0 2970 y FL(The)27 b(notion)f(of)h FC(exact)i(squar)l(es)34 b FL(replaces)25 b(the)i(notion)f(of)h(w)n (eak)f(pullbac)n(ks)e(in)j(the)g(preorder)e(setting)h(and)h(exact)g (squares)0 3070 y(will)19 b(pla)n(y)h(a)h(cen)n(tral)e(r^)-42 b(ole)20 b(in)h(our)g(extension)f(theorem.)33 b(Exact)21 b(squares)f(w)n(ere)g(in)n(tro)r(duced)h(and)g(studied)g(b)n(y)g(Ren)n (\023)-39 b(e)21 b(Guitart)0 3169 y(in)27 b([)120 3169 y SDict begin H.S end 120 3169 a Black FL(Gu)p Black 231 3113 a SDict begin H.R end 231 3113 a 231 3169 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.guitart) cvn H.B /ANN pdfmark end 231 3169 a FL(].)0 3314 y SDict begin H.S end 0 3314 a 0 3314 a SDict begin 12 H.A end 0 3314 a 0 3314 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.1) cvn /DEST pdfmark end 0 3314 a Black FM(De\014nition)k(3.1.)p Black 40 w FL(A)d(lax)e(square)g(in)h FI(Pre)1683 3607 y SDict begin H.S end 1683 3607 a 1754 3446 a FB(P)1936 3389 y Fz(p)1970 3397 y Fl(1)2069 3425 y Fy(/)p Fx(/)p 1869 3427 200 4 v 1708 3585 a Fz(p)1742 3593 y Fl(0)1799 3670 y Fy(\017)p Fx(\017)p 1798 3670 4 200 v 1933 3593 a FJ(\045)2094 3446 y FB(B)2158 3585 y Fz(g)2133 3670 y Fy(\017)p Fx(\017)p 2131 3670 V 1756 3753 a FB(A)1951 3797 y Fz(f)2073 3732 y Fy(/)p Fx(/)p 1867 3734 207 4 v 2098 3753 a FB(C)2217 3607 y SDict begin 12 H.A end 2217 3607 a 2217 3607 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.3) cvn /DEST pdfmark end 2217 3607 a Black 1512 w FL(\(3.3\))p Black 0 3938 a(is)f FC(exact)36 b FL(i\013)27 b(the)h(canonical)c(comparison)g(in)j FI(Rel)p FL(\()p FI(Pre)p FL(\))h(b)r(elo)n(w)e(is)h(an)g(iso)f(\(iden)n(tit)n(y\).)1623 4307 y SDict begin H.S end 1623 4307 a 1781 4155 a FB(P)1806 4273 y FA(U)p 1824 4279 4 100 v 1648 4302 a FE(\()p Fz(p)1708 4310 y Fl(0)1741 4302 y FE(\))1767 4310 y Fq(\005)1826 4379 y Fy(\017)p Fx(\017)p 1824 4379 V 1960 4302 a FJ(&)2121 4155 y FB(B)1990 4154 y FA(\025)p 1996 4136 100 4 v 1919 4094 a FE(\()p Fz(p)1979 4102 y Fl(1)2012 4094 y FE(\))2038 4069 y Fq(\005)1896 4134 y Fy(o)p Fx(o)p 1896 4136 V 2140 4273 a FA(U)p 2158 4279 4 100 v 2185 4294 a Fz(g)2217 4302 y Fq(\005)2160 4379 y Fy(\017)p Fx(\017)p 2158 4379 V 1783 4462 a FB(A)275 b(C)1991 4461 y FA(\025)p 1997 4443 104 4 v 1960 4511 a Fz(f)1999 4486 y Fq(\005)1894 4441 y Fy(o)p Fx(o)p 1894 4443 V 2277 4307 a SDict begin 12 H.A end 2277 4307 a 2277 4307 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.4) cvn /DEST pdfmark end 2277 4307 a Black 1452 w FL(\(3.4\))p Black 0 4675 a SDict begin H.S end 0 4675 a 0 4675 a SDict begin 12 H.A end 0 4675 a 0 4675 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.2) cvn /DEST pdfmark end 0 4675 a Black FM(Remark)42 b(3.2.)p Black 46 w FL(In)c(de\014ning)e(the)i (canonical)c(comparison,)i(w)n(e)h(use)h(the)g(adjunctions)e(\()p FF(p)2976 4687 y FE(1)3013 4675 y FL(\))3045 4687 y FJ(\005)3123 4675 y FK(a)j FL(\()p FF(p)3287 4687 y FE(1)3325 4675 y FL(\))3357 4645 y FJ(\005)3433 4675 y FL(and)e FF(f)3645 4687 y FJ(\005)3722 4675 y FK(a)i FF(f)3862 4645 y FJ(\005)0 4775 y FL(guaran)n(teed)26 b(b)n(y)h(Lemma)839 4775 y SDict begin H.S end 839 4775 a Black FL(2.5)p Black 945 4721 a SDict begin H.R end 945 4721 a 945 4775 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.2.5) cvn H.B /ANN pdfmark end 945 4775 a FL(.)125 4874 y(Using)f(the)i(form)n(ula)d(\()838 4874 y SDict begin H.S end 838 4874 a Black FL(2.1)p Black 944 4821 a SDict begin H.R end 944 4821 a 944 4874 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.1) cvn H.B /ANN pdfmark end 944 4874 a FL(\))j(w)n(e)f(obtain)f(an)i(equiv)-5 b(alen)n(t)25 b(criterion)g(for)i(exactness)f(namely)g(that)1260 5047 y SDict begin H.S end 1260 5047 a FB(C)14 b FL(\()p FF(f)9 b(a;)14 b(g)s(b)p FL(\))23 b(=)1713 4968 y Fu(_)1735 5143 y Fz(w)1819 5047 y FB(A)c FL(\()p FF(a;)14 b(p)2060 5059 y FE(0)2097 5047 y FF(w)r FL(\))20 b FK(^)e FB(B)s FL(\()p FF(p)2435 5059 y FE(1)2473 5047 y FF(w)r(;)c(b)p FL(\))2639 5047 y SDict begin 12 H.A end 2639 5047 a 2639 5047 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.5) cvn /DEST pdfmark end 2639 5047 a Black 1090 w FL(\(3.5\))p Black Black 1908 5400 a(10)p Black eop end end %%Page: 11 11 TeXDict begin HPSdict begin 11 10 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.11) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a SDict begin H.S end 0 83 a 0 83 a SDict begin 12 H.A end 0 83 a 0 83 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.3) cvn /DEST pdfmark end 0 83 a Black FM(Example)29 b(3.3.)p Black 40 w FL(W)-7 b(e)27 b(giv)n(e)e(examples)f(of)i(exact)h (squares)e(in)h FI(Pre)p FL(.)37 b(They)27 b(all)d(come)h(from)h (Guitart's)f(pap)r(er)i([)3477 83 y SDict begin H.S end 3477 83 a Black FL(Gu)p Black 3588 26 a SDict begin H.R end 3588 26 a 3588 83 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.guitart) cvn H.B /ANN pdfmark end 3588 83 a FL(],)g(Exam-)0 183 y(ple)g(1.14.)35 b(The)28 b(pro)r(ofs)f(follo)n(w)e(immediately)d (from)27 b(the)h(description)d(\()2271 183 y SDict begin H.S end 2271 183 a Black FL(3.5)p Black 2377 129 a SDict begin H.R end 2377 129 a 2377 183 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.5) cvn H.B /ANN pdfmark end 2377 183 a FL(\))j(ab)r(o)n(v)n(e.)0 222 y SDict begin H.S end 0 222 a 0 222 a SDict begin 12 H.A end 0 222 a 0 222 a SDict begin [/View [/XYZ H.V]/Dest (Item.20) cvn /DEST pdfmark end 0 222 a Black 101 329 a FL(1.)p Black 42 w(The)f(square)1847 476 y FB(A)2037 419 y Fz(f)2157 455 y Fy(/)p Fx(/)p 1957 457 200 4 v 1774 623 a FE(1)1807 632 y Fo(A)1890 700 y Fy(\017)p Fx(\017)p 1888 700 4 200 v 2022 623 a FJ(\045)2181 476 y FB(B)2246 623 y FE(1)2279 632 y Fo(B)2221 700 y Fy(\017)p Fx(\017)p 2219 700 V 1847 783 a FB(A)2037 828 y Fz(f)2157 762 y Fy(/)p Fx(/)p 1957 764 200 4 v 2181 783 a FB(B)208 965 y FL(where)g(the)h(comparison) 23 b(is)k(iden)n(tit)n(y)-7 b(,)26 b(is)g(alw)n(a)n(ys)f(exact)i(since) 1435 1136 y FB(B)s FL(\()p FF(f)9 b(a;)14 b(b)p FL(\))23 b(=)1855 1057 y Fu(_)1876 1231 y Fz(w)1961 1136 y FB(A)18 b FL(\()p FF(a;)c(w)r FL(\))20 b FK(^)f FB(B)s FL(\()p FF(f)9 b(w)r(;)14 b(b)p FL(\))208 1369 y(holds)26 b(b)n(y)h(the)h(Y)-7 b(oneda)27 b(Lemma.)35 b(Suc)n(h)28 b(a)f(square)f(is)h(called)e(a)i FC(Y)-6 b(one)l(da)30 b(squar)l(e)k FL(in)27 b([)2901 1369 y SDict begin H.S end 2901 1369 a Black FL(Gu)p Black 3012 1312 a SDict begin H.R end 3012 1312 a 3012 1369 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.guitart) cvn H.B /ANN pdfmark end 3012 1369 a FL(].)0 1418 y SDict begin H.S end 0 1418 a 0 1418 a SDict begin 12 H.A end 0 1418 a 0 1418 a SDict begin [/View [/XYZ H.V]/Dest (Item.21) cvn /DEST pdfmark end 0 1418 a Black 101 1525 a FL(2.)p Black 42 w(The)g(square)1844 1667 y FB(A)2008 1612 y FE(1)2041 1621 y Fo(A)2153 1646 y Fy(/)p Fx(/)p 1954 1648 200 4 v 1823 1814 a Fz(f)1886 1891 y Fy(\017)p Fx(\017)p 1885 1891 4 200 v 2021 1814 a FJ(\045)2178 1667 y FB(A)2246 1814 y Fz(f)2221 1891 y Fy(\017)p Fx(\017)p 2219 1891 V 1847 1974 a FB(B)2010 2016 y FE(1)2043 2025 y Fo(B)2157 1953 y Fy(/)p Fx(/)p 1951 1955 207 4 v 2182 1974 a FB(B)208 2151 y FL(where)g(the)h(comparison)23 b(is)k(iden)n(tit)n(y)-7 b(,)26 b(is)g(alw)n(a)n(ys)f(exact)i(since) 1435 2321 y FB(B)s FL(\()p FF(b;)14 b(f)9 b(a)p FL(\))23 b(=)1855 2242 y Fu(_)1876 2417 y Fz(w)1961 2321 y FB(B)s FL(\()p FF(b;)14 b(f)9 b(w)r FL(\))19 b FK(^)g FB(A)g FL(\()p FF(w)r(;)14 b(a)p FL(\))208 2554 y(holds)26 b(b)n(y)h(the)h(Y) -7 b(oneda)27 b(Lemma.)35 b(Again,)26 b(squares)g(of)i(this)f(form)f (are)g(called)g FC(Y)-6 b(one)l(da)30 b(squar)l(es)k FL(in)27 b([)3402 2554 y SDict begin H.S end 3402 2554 a Black FL(Gu)p Black 3513 2498 a SDict begin H.R end 3513 2498 a 3513 2554 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.guitart) cvn H.B /ANN pdfmark end 3513 2554 a FL(].)0 2603 y SDict begin H.S end 0 2603 a 0 2603 a SDict begin 12 H.A end 0 2603 a 0 2603 a SDict begin [/View [/XYZ H.V]/Dest (Item.22) cvn /DEST pdfmark end 0 2603 a Black 101 2711 a FL(3.)p Black 42 w(Ev)n(ery)e FC(c)l(omma)31 b(squar)l(e)1826 2854 y FF(f)9 b(=g)2050 2800 y Fz(d)2085 2808 y Fl(1)2183 2834 y Fy(/)p Fx(/)p 1984 2835 200 4 v 1801 3010 a Fz(d)1836 3018 y Fl(0)1892 3091 y Fy(\017)p Fx(\017)p 1891 3091 4 191 v 2037 3008 a FJ(\045)2208 2854 y FB(B)2273 3000 y Fz(g)2248 3091 y Fy(\017)p Fx(\017)p 2246 3091 4 212 v 1850 3174 a FB(A)2055 3219 y Fz(f)2188 3153 y Fy(/)p Fx(/)p 1960 3155 228 4 v 2213 3174 a FB(C)208 3354 y FL(is)26 b(exact.)0 3382 y SDict begin H.S end 0 3382 a 0 3382 a SDict begin 12 H.A end 0 3382 a 0 3382 a SDict begin [/View [/XYZ H.V]/Dest (Item.23) cvn /DEST pdfmark end 0 3382 a Black 101 3510 a FL(4.)p Black 42 w(Ev)n(ery)f FC(op-c)l(omma)31 b(squar)l(e)1820 3642 y FB(C)2023 3585 y Fz(g)2167 3621 y Fy(/)p Fx(/)p 1914 3622 254 4 v 1791 3793 a Fz(f)1854 3874 y Fy(\017)p Fx(\017)p 1853 3874 4 208 v 2010 3793 a FJ(\045)2192 3642 y FB(B)2257 3793 y Fz(i)2280 3801 y Fl(1)2232 3874 y Fy(\017)p Fx(\017)p 2230 3874 V 1812 3957 a FB(A)1994 3999 y Fz(i)2017 4007 y Fl(0)2121 3936 y Fy(/)p Fx(/)p 1922 3938 200 4 v 2146 3957 a FF(f)c(.)18 b(g)208 4132 y FL(is)26 b(exact.)0 4160 y SDict begin H.S end 0 4160 a 0 4160 a SDict begin 12 H.A end 0 4160 a 0 4160 a SDict begin [/View [/XYZ H.V]/Dest (Item.24) cvn /DEST pdfmark end 0 4160 a Black 101 4288 a FL(5.)p Black 42 w(The)h(square)1870 4430 y FB(A)2034 4375 y FE(1)2067 4384 y Fo(A)2179 4409 y Fy(/)p Fx(/)p 1980 4410 200 4 v 1797 4577 a FE(1)1830 4586 y Fo(A)1912 4654 y Fy(\017)p Fx(\017)p 1911 4654 4 200 v 2047 4577 a FJ(\045)2204 4430 y FB(A)2272 4577 y Fz(f)2247 4654 y Fy(\017)p Fx(\017)p 2246 4654 V 1870 4737 a FB(A)2062 4781 y Fz(f)2183 4716 y Fy(/)p Fx(/)p 1980 4718 203 4 v 2208 4737 a FB(B)208 4923 y FL(\(where)35 b(the)h(comparison)31 b(is)k(iden)n(tit)n(y\))f(is)g(exact)h(i\013)g FF(f)44 b FL(is)35 b(an)g FC(or)l(der-emb)l(e)l(dding)7 b FL(,)39 b(i.e.,)e(i\013)e(the)h(follo)n(wing)31 b(holds:)208 5023 y FF(f)9 b(a)22 b FK(\024)h FF(f)9 b(a)506 4993 y FJ(0)556 5023 y FL(i\013)27 b FF(a)c FK(\024)g FF(a)854 4993 y FJ(0)877 5023 y FL(.)208 5151 y(Suc)n(h)k FF(f)9 b FL('s)27 b(can)g(also)f(b)r(e)i(called)d FC(ful)t(ly)31 b(faithful)9 b FL(.)p Black 1908 5400 a(11)p Black eop end end %%Page: 12 12 TeXDict begin HPSdict begin 12 11 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.12) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.25) cvn /DEST pdfmark end 0 0 a Black 101 83 a FL(6.)p Black 42 w(The)27 b(square)1817 203 y FB(A)2011 157 y Fz(e)2127 182 y Fy(/)p Fx(/)p 1928 184 200 4 v 1803 348 a Fz(e)1860 427 y Fy(\017)p Fx(\017)p 1858 427 4 200 v 1992 350 a FJ(\045)2152 203 y FB(B)2216 350 y FE(1)2249 359 y Fo(B)2191 427 y Fy(\017)p Fx(\017)p 2189 427 V 1820 510 a FB(B)1981 552 y FE(1)2014 561 y Fo(B)2127 489 y Fy(/)p Fx(/)p 1924 491 203 4 v 2152 510 a FB(B)208 697 y FL(\(where)g(the)h(comparison)c(is)i(iden)n(tit)n(y\))g(is)h (exact)g(i\013)g FF(e)g FL(is)g FC(absolutely)k(dense)6 b FL(,)28 b(i.e.,)f(i\013)1440 882 y FB(B)s FL(\()p FF(b;)14 b(b)1659 847 y FJ(0)1683 882 y FL(\))23 b(=)1826 803 y Fu(_)1854 977 y Fz(a)1932 882 y FB(B)s FL(\()p FF(b;)14 b(ea)p FL(\))19 b FK(^)f FB(B)s FL(\()p FF(ea;)c(b)2588 847 y FJ(0)2612 882 y FL(\))p FF(:)208 1124 y FL(See,)27 b(e.g.,)g([)576 1124 y SDict begin H.S end 576 1124 a Black FL(ABSV)p Black 806 1067 a SDict begin H.R end 806 1067 a 806 1124 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.absv) cvn H.B /ANN pdfmark end 806 1124 a FL(])h(and)f([)1041 1124 y SDict begin H.S end 1041 1124 a Black FL(BV)p Black 1162 1067 a SDict begin H.R end 1162 1067 a 1162 1124 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.bv) cvn H.B /ANN pdfmark end 1162 1124 a FL(])h(for)f(more)f(details)f(on)j (absolutely)c(dense)k(maps.)0 1175 y SDict begin H.S end 0 1175 a 0 1175 a SDict begin 12 H.A end 0 1175 a 0 1175 a SDict begin [/View [/XYZ H.V]/Dest (Item.26) cvn /DEST pdfmark end 0 1175 a Black 101 1284 a FL(7.)p Black 42 w(The)f(square)1860 1431 y FB(X)2069 1374 y Fz(f)2191 1410 y Fy(/)p Fx(/)p 1985 1412 207 4 v 1784 1578 a FE(1)1817 1587 y Fo(X)1910 1655 y Fy(\017)p Fx(\017)p 1908 1655 4 200 v 2051 1578 a FJ(\045)2216 1431 y FB(A)2284 1576 y Fz(u)2259 1655 y Fy(\017)p Fx(\017)p 2257 1655 V 1860 1738 a FB(X)2034 1780 y FE(1)2067 1789 y Fo(X)2184 1717 y Fy(/)p Fx(/)p 1985 1719 200 4 v 2209 1738 a FB(X)208 1921 y FL(is)d(exact)h(i\013)f FF(f)32 b FK(a)23 b FF(u)f FL(:)i FB(A)41 b FK(\000)-14 b(!)23 b FB(X)48 b FL(holds.)34 b(Moreo)n(v)n(er,)23 b(the)j(comparison)c(in)i(the)i(ab)r(o)n(v)n(e)e (square)g(is)g(the)i(unit)f(of)g FF(f)32 b FK(a)22 b FF(u)p FL(.)0 1967 y SDict begin H.S end 0 1967 a 0 1967 a SDict begin 12 H.A end 0 1967 a 0 1967 a SDict begin [/View [/XYZ H.V]/Dest (Item.27) cvn /DEST pdfmark end 0 1967 a Black 101 2081 a FL(8.)p Black 42 w(The)27 b(square)1814 2223 y FB(A)1982 2168 y FE(1)2015 2177 y Fo(A)2131 2202 y Fy(/)p Fx(/)p 1925 2203 207 4 v 1793 2368 a Fz(u)1857 2447 y Fy(\017)p Fx(\017)p 1855 2447 4 200 v 1995 2370 a FJ(\045)2156 2223 y FB(A)2224 2370 y FE(1)2257 2379 y Fo(A)2199 2447 y Fy(\017)p Fx(\017)p 2197 2447 V 1807 2530 a FB(X)2012 2574 y Fz(f)2131 2509 y Fy(/)p Fx(/)p 1932 2511 200 4 v 2156 2530 a FB(A)208 2718 y FL(is)k(exact)h(i\013)g FF(f)39 b FK(a)31 b FF(u)g FL(:)g FB(A)50 b FK(\000)-14 b(!)31 b FB(X)54 b FL(holds.)c(Moreo)n(v)n (er,)31 b(the)i(comparison)c(in)i(the)i(ab)r(o)n(v)n(e)e(square)g(is)h (the)h(counit)e(of)208 2817 y FF(f)g FK(a)23 b FF(u)p FL(.)0 2864 y SDict begin H.S end 0 2864 a 0 2864 a SDict begin 12 H.A end 0 2864 a 0 2864 a SDict begin [/View [/XYZ H.V]/Dest (Item.28) cvn /DEST pdfmark end 0 2864 a Black 101 2977 a FL(9.)p Black 42 w(The)k(square)1854 3124 y FB(X)1954 3094 y FJ(0)2086 3067 y Fz(f)2208 3103 y Fy(/)p Fx(/)p 2002 3105 207 4 v 1767 3270 a FE(1)1800 3286 y Fo(X)1864 3274 y Fq(0)1915 3348 y Fy(\017)p Fx(\017)p 1914 3348 4 200 v 2063 3274 a FJ(\045)2233 3124 y FB(A)2301 3272 y Fz(u)2276 3353 y Fy(\017)p Fx(\017)p 2274 3353 4 204 v 1854 3436 a FB(X)1954 3406 y FJ(0)2086 3478 y Fz(j)2201 3415 y Fy(/)p Fx(/)p 2002 3417 200 4 v 2226 3436 a FB(X)208 3622 y FL(is)f(exact)h(i\013)g FF(f)32 b FK(a)733 3634 y Fz(j)791 3622 y FF(u)22 b FL(:)h FB(A)42 b FK(\000)-14 b(!)23 b FB(X)50 b FL(holds,)26 b(i.e.,)h(i\013)g FF(f)36 b FL(is)27 b(a)g(left)g(adjoin)n(t)f(of)i FF(u)f FC(r)l(elative)k(to)i FF(j)5 b FL(.)208 3752 y(In)27 b(general,)f(relativ)n(e)e(adjoin)n(tness)i(means)g(the)i(existence)e (of)i(an)f(isomorphism)1621 3919 y FB(X)22 b FL(\()p FF(j)5 b(x)1839 3885 y FJ(0)1863 3919 y FF(;)14 b(ua)p FL(\))2047 3897 y FK(\030)2047 3924 y FL(=)2135 3919 y FB(A)k FL(\()p FF(f)9 b(x)2349 3885 y FJ(0)2373 3919 y FF(;)14 b(a)p FL(\))208 4087 y(natural)25 b(in)i FF(x)642 4057 y FJ(0)694 4087 y FL(and)g FF(a)p FL(,)h(and)f(due)h(to)1374 4267 y FB(A)19 b FL(\()p FF(f)9 b(x)1589 4233 y FJ(0)1612 4267 y FF(;)14 b(a)p FL(\))1748 4245 y FK(\030)1748 4271 y FL(=)1836 4188 y Fu(_)1857 4362 y Fz(w)1942 4267 y FB(X)2042 4233 y FJ(0)2065 4267 y FL(\()p FF(w)r(;)g(x)2242 4233 y FJ(0)2267 4267 y FL(\))19 b FK(^)f FB(A)h FL(\()p FF(f)9 b(w)r(;)14 b(a)p FL(\))208 4505 y(this)26 b(means)h(precisely)d (the)k(exactness)f(of)g(the)h(ab)r(o)n(v)n(e)f(square.)0 4551 y SDict begin H.S end 0 4551 a 0 4551 a SDict begin 12 H.A end 0 4551 a 0 4551 a SDict begin [/View [/XYZ H.V]/Dest (Item.29) cvn /DEST pdfmark end 0 4551 a Black 60 4665 a FL(10.)p Black 41 w(The)g(square)1843 4810 y FB(A)2047 4753 y Fz(j)2171 4789 y Fy(/)p Fx(/)p 1954 4791 218 4 v 1822 4963 a Fz(h)1886 5034 y Fy(\017)p Fx(\017)p 1884 5034 4 200 v 2028 4957 a FJ(\045)2196 4810 y FB(B)2260 4963 y Fz(l)2235 5034 y Fy(\017)p Fx(\017)p 2234 5034 V 1836 5117 a FB(X)2010 5158 y FE(1)2043 5167 y Fo(X)2160 5096 y Fy(/)p Fx(/)p 1961 5098 200 4 v 2185 5117 a FB(X)p Black 1908 5400 a FL(12)p Black eop end end %%Page: 13 13 TeXDict begin HPSdict begin 13 12 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.13) cvn /DEST pdfmark end -8 -8 a Black Black 208 83 a FL(is)26 b(exact)h(i\013)g(the)h(comparison)c(exhibits)i FF(l)j FL(as)e(an)g FC(absolute)35 b FL(left)27 b(Kan)g(extension)f(of) i FF(h)f FL(along)e FF(j)5 b FL(.)37 b(In)28 b(fact,)1424 273 y FB(X)22 b FL(\()p FF(x;)14 b(l)r(b)p FL(\))23 b(=)1846 194 y Fu(_)1874 368 y Fz(a)1952 273 y FB(X)f FL(\()p FF(x;)14 b(ha)p FL(\))19 b FK(^)g FB(B)s FL(\()p FF(j)5 b(a;)14 b(b)p FL(\))208 520 y(asserts)26 b(precisely)e(that)0 585 y SDict begin H.S end 0 585 a 0 585 a SDict begin 12 H.A end 0 585 a 0 585 a SDict begin [/View [/XYZ H.V]/Dest (Item.30) cvn /DEST pdfmark end 0 585 a Black 243 684 a FL(\(a\))p Black 41 w FF(l)29 b FL(is)e(a)g(left)g(Kan)g (extension)f(of)i FF(h)f FL(along)f FF(j)5 b FL(.)390 800 y(F)-7 b(or)27 b(an)n(y)g FF(k)f FL(:)d FB(B)k FK(\000)-14 b(!)23 b FB(X)49 b FL(w)n(e)28 b(need)f(to)h(pro)n(v)n(e)e FF(l)e FK(\000)-14 b(!)23 b FF(k)30 b FL(i\013)e FF(h)23 b FK(\000)-15 b(!)23 b FF(k)f FK(\001)c FF(j)5 b FL(.)0 847 y SDict begin H.S end 0 847 a 0 847 a SDict begin 12 H.A end 0 847 a 0 847 a SDict begin [/View [/XYZ H.V]/Dest (Item.31) cvn /DEST pdfmark end 0 847 a Black 458 930 a FL(i.)p Black 40 w(Supp)r(ose)24 b FF(l)r(b)e FK(\024)h FF(k)s(b)g FL(for)h(all)d FF(b)p FL(.)36 b(Cho)r(ose)23 b(an)n(y)g FF(a)p FL(.)35 b(Then)24 b FF(ha)f FK(\024)g FF(l)r(j)5 b(a)23 b FL(b)n(y)g(the)i(square)d(ab)r(o)n(v)n(e.)34 b(Since)23 b FF(l)r(j)5 b(a)23 b FK(\024)f FF(k)s(j)5 b(a)545 1030 y FL(b)n(y)28 b(assumption,)d(hence)j FF(ha)22 b FK(\024)h FF(k)s(j)5 b(a)p FL(.)0 1062 y SDict begin H.S end 0 1062 a 0 1062 a SDict begin 12 H.A end 0 1062 a 0 1062 a SDict begin [/View [/XYZ H.V]/Dest (Item.32) cvn /DEST pdfmark end 0 1062 a Black 435 1145 a FL(ii.)p Black 39 w(Supp)r(ose)28 b FF(ha)23 b FK(\024)f FF(k)s(j)5 b(a)27 b FL(for)g(all)e FF(a)p FL(.)37 b(T)-7 b(o)26 b(pro)n(v)n(e)g FF(l)r(b)c FK(\024)h FF(k)s(b)k FL(for)f(all)f FF(b)p FL(,)i(it)g(su\016ces)g(to)g(pro)n(v)n(e)f(that)h FF(x)d FK(\024)e FF(l)r(b)27 b FL(implies)545 1245 y FF(x)33 b FK(\024)g FF(k)s(b)p FL(,)h(for)f(all)e FF(x)p FL(.)54 b(Supp)r(ose)33 b FF(x)g FK(\024)f FF(l)r(b)p FL(,)i(i.e.,)g FB(X)22 b FL(\()p FF(x;)14 b(l)r(b)p FL(\))33 b(=)f(1.)53 b(Hence)2844 1183 y Fu(W)2913 1270 y Fz(a)2967 1245 y FB(X)22 b FL(\()p FF(x;)14 b(ha)p FL(\))23 b FK(^)f FB(B)s FL(\()p FF(j)5 b(a;)14 b(b)p FL(\))33 b(=)f(1.)545 1344 y(Cho)r(ose)h FF(a)g FL(to)h(witness)e FF(x)h FK(\024)g FF(ha)g FL(and)g FF(j)5 b(a)33 b FK(\024)f FF(b)p FL(.)54 b(F)-7 b(rom)32 b(our)h(assumption)e(w)n(e)i(obtain)f FF(x)h FK(\024)f FF(k)s(j)5 b(a)p FL(,)35 b(hence)545 1444 y FF(x)24 b FK(\024)f FF(k)s(b)p FL(.)0 1471 y SDict begin H.S end 0 1471 a 0 1471 a SDict begin 12 H.A end 0 1471 a 0 1471 a SDict begin [/View [/XYZ H.V]/Dest (Item.33) cvn /DEST pdfmark end 0 1471 a Black 238 1575 a FL(\(b\))p Black 42 w FF(l)29 b FL(is)e(an)g(absolute)f(left)h (Kan)g(extension)f(of)i FF(h)f FL(along)f FF(j)5 b FL(.)390 1690 y(W)-7 b(e)29 b(need)f(to)h(pro)n(v)n(e)d(that)j(for)f(an)n(y)f FF(f)33 b FL(:)25 b FB(X)46 b FK(\000)-14 b(!)24 b FB(X)2025 1660 y FJ(0)2049 1690 y FL(,)k FF(f)g FK(\001)19 b FF(l)30 b FL(is)d(a)h(left)g(Kan)g(extension)f(of)h FF(f)f FK(\001)19 b FF(h)29 b FL(along)d FF(j)5 b FL(.)39 b(That)390 1790 y(is,)27 b(for)g(an)n(y)g FF(k)f FL(:)d FB(B)j FK(\000)-14 b(!)23 b FB(X)1254 1760 y FJ(0)1305 1790 y FL(w)n(e)k(need)h(to)g(pro)n (v)n(e)e FF(f)h FK(\001)18 b FF(l)25 b FK(\000)-15 b(!)23 b FF(k)31 b FL(i\013)c FF(f)g FK(\001)19 b FF(h)k FK(\000)-15 b(!)23 b FF(k)f FK(\001)c FF(j)5 b FL(.)390 1905 y(This)27 b(is)f(pro)n(v)n(ed)g(in)h(the)h(same)e(manner)g(as)h(ab)r(o)n(v)n(e.) 208 2069 y(Observ)n(e)f(that)i(item)896 2069 y SDict begin H.S end 896 2069 a Black FL(7)p Black 938 2015 a SDict begin H.R end 938 2015 a 938 2069 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (Item.26) cvn H.B /ANN pdfmark end 938 2069 a 27 w FL(ab)r(o)n(v)n(e)f(is)g(a)g(sp)r(ecial)e(case)i(of)h (absolute)e(Kan)h(extensions)f(b)n(y)i(B)n(\023)-39 b(enab)r(ou's)26 b(Theorem:)35 b FF(f)d FK(a)23 b FF(u)208 2169 y FL(holds)j(if)h(the)h (unit)f(exhibits)f FF(u)h FL(as)g(an)g(absolute)f(left)i(Kan)e (extension)h(of)g(iden)n(tit)n(y)f(along)f FF(f)9 b FL(.)0 2331 y SDict begin H.S end 0 2331 a 0 2331 a SDict begin 12 H.A end 0 2331 a 0 2331 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.4) cvn /DEST pdfmark end 0 2331 a Black FM(Example)35 b(3.4.)p Black 43 w FL(Ev)n(ery)30 b(square)h(\()1133 2331 y SDict begin H.S end 1133 2331 a Black FL(3.3)p Black 1240 2277 a SDict begin H.R end 1240 2277 a 1240 2331 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 1240 2331 a FL(\))h(where)f FF(f)41 b FL(and)32 b FF(p)1838 2343 y FE(1)1907 2331 y FL(are)f FC(left)41 b FL(adjoin)n(ts,)31 b(is)g(exact)h(i\013)f FF(p)3002 2343 y FE(0)3061 2331 y FK(\001)21 b FF(p)3147 2300 y Fz(r)3147 2351 y FE(1)3215 2331 y FL(=)30 b FF(f)3360 2300 y Fz(r)3418 2331 y FK(\001)21 b FF(g)s FL(,)33 b(where)e(w)n(e)0 2430 y(denote)d(b)n(y)f FF(f)433 2400 y Fz(r)497 2430 y FL(and)g FF(p)700 2400 y Fz(r)700 2451 y FE(1)765 2430 y FL(the)h(resp)r(ectiv)n(e)e(righ)n(t)g(adjoin)n(ts.)125 2530 y(This)38 b(is)g(pro)n(v)n(ed)g(as)g(follo)n(ws.)69 b(Firstly)-7 b(,)40 b(the)f(comparison)d FF(f)f FK(\001)26 b FF(p)2228 2542 y FE(0)2307 2530 y FK(\000)-14 b(!)43 b FF(g)28 b FK(\001)f FF(p)2644 2542 y FE(1)2720 2530 y FL(is)38 b(equiv)-5 b(alen)n(t)37 b(to)i(the)h(comparison)0 2629 y FF(p)42 2641 y FE(0)97 2629 y FK(\001)19 b FF(p)181 2599 y Fz(r)181 2650 y FE(1)241 2629 y FK(\000)-14 b(!)23 b FF(f)448 2599 y Fz(r)503 2629 y FK(\001)18 b FF(g)30 b FL(due)e(to)g(adjunctions)e FF(f)32 b FK(a)23 b FF(f)1515 2599 y Fz(r)1579 2629 y FL(and)k FF(p)1782 2641 y FE(1)1842 2629 y FK(a)c FF(p)1958 2599 y Fz(r)1958 2650 y FE(1)1995 2629 y FL(.)37 b(F)-7 b(urther,)27 b(w)n(e)h(ha)n(v)n(e)694 2745 y Fu(_)716 2919 y Fz(w)800 2824 y FB(A)19 b FL(\()p FF(a;)14 b(p)1041 2836 y FE(0)1078 2824 y FF(w)r FL(\))20 b FK(^)e FB(B)s FL(\()p FF(p)1416 2836 y FE(1)1454 2824 y FF(w)r(;)c(b)p FL(\))24 b(=)1732 2745 y Fu(_)1753 2919 y Fz(w)1838 2824 y FB(A)18 b FL(\()p FF(a;)c(p)2078 2836 y FE(0)2115 2824 y FF(w)r FL(\))20 b FK(^)f FB(P)7 b FL(\()p FF(w)r(;)14 b(p)2565 2789 y Fz(r)2565 2844 y FE(1)2602 2824 y FF(b)p FL(\))23 b(=)g FB(A)c FL(\()p FF(a;)14 b(p)3022 2836 y FE(0)3059 2824 y FF(p)3101 2789 y Fz(r)3101 2844 y FE(1)3138 2824 y FF(b)p FL(\))0 3071 y(and)1526 3171 y FB(C)g FL(\()p FF(f)9 b(a;)14 b(g)s(b)p FL(\))22 b(=)h FB(A)18 b FL(\()p FF(a;)c(f)2227 3137 y Fz(r)2264 3171 y FF(g)s(b)p FL(\))0 3317 y(It)28 b(follo)n(ws)d(that) i(the)h(square)f(\()979 3317 y SDict begin H.S end 979 3317 a Black FL(3.3)p Black 1085 3264 a SDict begin H.R end 1085 3264 a 1085 3317 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 1085 3317 a FL(\))h(is)e(exact)i(i\013)1473 3495 y FB(A)19 b FL(\()p FF(a;)14 b(p)1714 3507 y FE(0)1751 3495 y FF(p)1793 3461 y Fz(r)1793 3515 y FE(1)1830 3495 y FF(b)p FL(\))23 b(=)f FB(A)d FL(\()p FF(a;)14 b(f)2257 3461 y Fz(r)2293 3495 y FF(g)s(b)p FL(\))p FF(:)0 3672 y FL(By)27 b(the)h(Y)-7 b(oneda)27 b(Lemma,)f(this)h(is)f(equiv)-5 b(alen)n(t)26 b(to)h FF(p)1671 3684 y FE(0)1727 3672 y FK(\001)18 b FF(p)1810 3642 y Fz(r)1810 3693 y FE(1)1870 3672 y FL(=)23 b FF(f)2008 3642 y Fz(r)2063 3672 y FK(\001)18 b FF(g)s FL(.)0 3834 y SDict begin H.S end 0 3834 a 0 3834 a SDict begin 12 H.A end 0 3834 a 0 3834 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.5) cvn /DEST pdfmark end 0 3834 a Black FM(Example)30 b(3.5.)p Black 40 w FL(If)e(the)g(square)f(on)g (the)h(left)f(is)g(exact,)g(then)h(so)f(is)f(the)i(square)f(on)g(the)h (righ)n(t:)1154 4071 y FB(P)1336 4014 y Fz(p)1370 4022 y Fl(1)1469 4051 y Fy(/)p Fx(/)p 1270 4052 200 4 v 1108 4211 a Fz(p)1142 4219 y Fl(0)1200 4296 y Fy(\017)p Fx(\017)p 1198 4296 4 200 v 1333 4219 a FJ(\045)1494 4071 y FB(B)1558 4211 y Fz(g)1533 4296 y Fy(\017)p Fx(\017)p 1532 4296 V 1157 4379 a FB(A)1351 4423 y Fz(f)1474 4358 y Fy(/)p Fx(/)p 1267 4359 207 4 v 1499 4379 a FB(C)2172 4071 y(P)2263 4041 y Fw(op)2420 4008 y Fz(p)2454 3980 y Fm(op)2454 4026 y Fl(0)2565 4051 y Fy(/)p Fx(/)p 2366 4052 200 4 v 2141 4218 a Fz(p)2175 4190 y Fm(op)2175 4236 y Fl(1)2257 4296 y Fy(\017)p Fx(\017)p 2255 4296 4 200 v 2431 4219 a FJ(\045)2590 4071 y FB(A)2675 4041 y Fw(op)2696 4220 y Fz(f)2735 4195 y Fm(op)2672 4296 y Fy(\017)p Fx(\017)p 2670 4296 V 2178 4379 a FB(B)2256 4348 y Fw(op)2421 4426 y Fz(g)2455 4401 y Fm(op)2573 4358 y Fy(/)p Fx(/)p 2360 4359 214 4 v 2598 4379 a FB(C)2667 4348 y Fw(op)0 4610 y FL(T)-7 b(o)27 b(pro)n(v)n(e)f(the)i(claim,)d(b)n(y)i(\()881 4610 y SDict begin H.S end 881 4610 a Black FL(3.5)p Black 987 4557 a SDict begin H.R end 987 4557 a 987 4610 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.5) cvn H.B /ANN pdfmark end 987 4610 a FL(\),)h(w)n(e)g(need)1025 4805 y FB(C)1095 4770 y Fw(op)1172 4805 y FL(\()p FF(g)1247 4770 y Fw(op)1325 4805 y FF(b;)14 b(f)1448 4770 y Fw(op)1525 4805 y FF(a)p FL(\))23 b(=)1712 4726 y Fu(_)1733 4900 y Fz(w)1818 4805 y FB(B)1896 4770 y Fw(op)1974 4805 y FL(\()p FF(b;)14 b(p)2121 4765 y Fw(op)2121 4827 y FE(1)2199 4805 y FF(w)r FL(\))19 b FK(^)g FB(A)2470 4770 y Fw(op)2548 4805 y FL(\()p FF(p)2622 4765 y Fw(op)2622 4827 y FE(0)2700 4805 y FF(w)r(;)14 b(a)p FL(\))0 5051 y(But)1436 5151 y FB(C)1505 5117 y Fw(op)1583 5151 y FL(\()p FF(g)1658 5117 y Fw(op)1735 5151 y FF(b;)g(f)1858 5117 y Fw(op)1935 5151 y FF(a)p FL(\))23 b(=)g FB(C)14 b FL(\()p FF(f)9 b(a;)14 b(g)s(b)p FL(\))p Black 1908 5400 a(13)p Black eop end end %%Page: 14 14 TeXDict begin HPSdict begin 14 13 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.14) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a FL(and)850 104 y Fu(_)871 278 y Fz(w)956 183 y FB(B)1034 148 y Fw(op)1112 183 y FL(\()p FF(b;)14 b(p)1259 143 y Fw(op)1259 205 y FE(1)1337 183 y FF(w)r FL(\))19 b FK(^)g FB(A)1609 148 y Fw(op)1686 183 y FL(\()p FF(p)1760 143 y Fw(op)1760 205 y FE(0)1838 183 y FF(w)r(;)14 b(a)p FL(\))24 b(=)2124 104 y Fu(_)2145 278 y Fz(w)2230 183 y FB(A)18 b FL(\()p FF(a;)c(p)2470 195 y FE(0)2507 183 y FF(w)r FL(\))20 b FK(^)f FB(B)s FL(\()p FF(p)2846 195 y FE(1)2884 183 y FF(w)r(;)14 b(b)p FL(\))0 401 y(and)27 b(this)g(\014nishes)g(the)h(pro)r(of.)0 565 y SDict begin H.S end 0 565 a 0 565 a SDict begin 12 H.A end 0 565 a 0 565 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.6) cvn /DEST pdfmark end 0 565 a Black FM(Lemma)23 b(3.6.)p Black 35 w FC(Supp)l(ose)i(that)g FL(\()p FF(d)1068 535 y Fz(S)1068 586 y FE(0)1117 565 y FF(;)14 b FB(E)1216 535 y Fz(S)1264 565 y FF(;)g(d)1344 535 y Fz(S)1344 586 y FE(1)1392 565 y FL(\))25 b FC(and)g FL(\()p FF(d)1680 535 y Fz(R)1680 586 y FE(0)1735 565 y FF(;)14 b FB(E)1834 535 y Fz(R)1888 565 y FF(;)g(d)1968 535 y Fz(R)1968 586 y FE(1)2023 565 y FL(\))25 b FC(ar)l(e)g(two-side)l(d)h(discr)l(ete)f (\014br)l(ations.)37 b(Then)26 b(the)f(pul)t(lb)l(ack)1591 782 y FB(E)1653 752 y Fz(S)1719 782 y FK(\016)18 b FB(E)1841 752 y Fz(R)1989 725 y(q)2019 733 y Fl(1)2120 761 y Fy(/)p Fx(/)p 1921 763 200 4 v 1655 927 a Fz(q)1685 935 y Fl(0)1743 1006 y Fy(\017)p Fx(\017)p 1741 1006 4 200 v 2145 782 a FB(E)2207 752 y Fz(R)2228 939 y(d)2263 914 y Fp(R)2263 956 y Fl(0)2203 1018 y Fy(\017)p Fx(\017)p 2201 1018 4 211 v 1688 1101 a FB(E)1750 1071 y Fz(S)1943 1158 y(d)1978 1133 y Fp(S)1978 1175 y Fl(1)2139 1080 y Fy(/)p Fx(/)p 1823 1082 316 4 v 2164 1101 a FB(B)0 1347 y FC(c)l(onsider)l(e)l(d)31 b(as)f(a)g(lax)g(c)l(ommutative)g(squar)l(e)g(wher)l(e)g(the)g(c)l(omp) l(arison)h(is)f(identity,)h(is)f(exact.)p Black 0 1511 a(Pr)l(o)l(of.)p Black 43 w FL(Supp)r(ose)e(that)g FF(d)809 1481 y Fz(S)809 1531 y FE(1)857 1511 y FL(\()p FF(e)p FL(\))23 b FK(\024)g FF(d)1114 1481 y Fz(R)1114 1531 y FE(0)1169 1511 y FL(\()p FF(f)9 b FL(\))27 b(holds.)36 b(Then)28 b(w)n(e)f(ha)n(v)n(e)f(a)i(situation)1558 1743 y FF(c)1703 1697 y Fz(e)1818 1722 y Fy(/)p Fx(/)1778 1723 y Fk(/o)1719 1722 y(/o)1660 1721 y(/o)1843 1743 y FF(b)23 b FK(\024)g FF(b)2026 1713 y FJ(0)2154 1686 y Fz(f)2273 1722 y Fy(/)p Fx(/)2232 1723 y Fk(/o)2173 1722 y(/o)2114 1721 y(/o)2298 1743 y FF(a)0 1938 y FL(and)k(there)h (exists)e FF(w)k FL(in)d FB(E)851 1908 y Fz(S)918 1938 y FK(\016)18 b FB(E)1040 1908 y Fz(R)1122 1938 y FL(of)28 b(the)g(form)1632 2149 y FF(c)1765 2104 y Fz(e)1796 2079 y Fq(0)1892 2129 y Fy(/)p Fx(/)1851 2130 y Fk(/o)1792 2129 y(/o)1733 2127 y(/o)1917 2149 y FF(b)1953 2119 y FJ(0)2081 2092 y Fz(f)2200 2129 y Fy(/)p Fx(/)2159 2130 y Fk(/o)2100 2129 y(/o)2041 2127 y(/o)2225 2149 y FF(a)0 2330 y FL(that)g(clearly)c(satis\014es)i FF(e)d FK(\024)f FF(p)942 2342 y FE(0)979 2330 y FL(\()p FF(e)1050 2300 y FJ(0)1074 2330 y FF(;)14 b(f)9 b FL(\))27 b(and)h FF(p)1424 2342 y FE(1)1461 2330 y FL(\()p FF(e)1532 2300 y FJ(0)1555 2330 y FF(;)14 b(f)9 b FL(\))23 b FK(\024)f FF(f)9 b FL(.)p 3839 2330 4 57 v 3843 2277 50 4 v 3843 2330 V 3893 2330 4 57 v 125 2535 a(Giv)n(en)26 b(monotone)f(relations)32 b FB(A)1280 2534 y FA(\025)p 1186 2516 100 4 v 1261 2489 a Fz(R)1385 2514 y Fy(/)p Fx(/)p 1286 2516 V 1394 2535 a FB(B)39 b FL(and)c FB(B)1858 2534 y FA(\025)p 1764 2516 V 1842 2489 a Fz(S)1964 2514 y Fy(/)p Fx(/)p 1864 2516 V 1972 2535 a FB(C)22 b FL(,)28 b(the)f(t)n(w)n(o-sided)e (\014bration)h(corresp)r(onding)e(to)j(the)h(com-)0 2635 y(p)r(osition)22 b FF(S)17 b FK(\001)12 b FF(R)25 b FL(is)e(the)i(comp) r(osition)c(of)j(the)h(\014brations)d(corresp)r(onding)g(to)i FF(S)29 b FL(and)c FF(R)g FL(as)e(describ)r(ed)h(in)f(Section)3582 2635 y SDict begin H.S end 3582 2635 a Black FL(2.D)p Black 3710 2578 a SDict begin H.R end 3710 2578 a 3710 2635 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (subsection.2.4) cvn H.B /ANN pdfmark end 3710 2635 a FL(.)h(The)0 2734 y(prop)r(erties)i (describ)r(ed)g(in)h(the)h(next)g(Corollary)23 b(are)j(essen)n(tial)f (for)i(the)h(pro)r(of)f(of)h(Theorem)2954 2734 y SDict begin H.S end 2954 2734 a Black FL(4.1)p Black 3060 2681 a SDict begin H.R end 3060 2681 a 3060 2734 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.4.1) cvn H.B /ANN pdfmark end 3060 2734 a FL(.)0 2898 y SDict begin H.S end 0 2898 a 0 2898 a SDict begin 12 H.A end 0 2898 a 0 2898 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3.7) cvn /DEST pdfmark end 0 2898 a Black FM(Corollary)33 b(3.7.)p Black 40 w FC(F)-6 b(orm,)30 b(for)h(a)f(p)l(air)h FF(R)q FC(,)f FF(S)5 b FC(,)30 b(of)g(monotone)g(r)l(elations)h(the)f(fol)t (lowing)i(c)l(ommutative)e(diagr)l(am)1853 3098 y FB(E)1915 3068 y Fz(S)s FJ(\001)p Fz(R)1147 3161 y Fj(G)q(F)p 1230 3079 598 4 v 984 3538 a Fz(d)1019 3513 y Fp(S)r Fq(\001)p Fp(R)1019 3555 y Fl(0)1147 3817 y Fy(\017)p Fx(\017)p 1146 3817 4 657 v 2670 3161 a Fj(E)o(D)p 2058 3079 612 4 v 2778 3538 a Fz(d)2813 3513 y Fp(S)r Fq(\001)p Fp(R)2813 3555 y Fl(1)2753 3817 y Fy(\017)p Fx(\017)p 2751 3817 4 657 v 1790 3368 a FB(E)1852 3337 y Fz(S)1919 3368 y FK(\016)18 b FB(E)2041 3337 y Fz(R)1650 3445 y(q)1680 3453 y Fl(0)1566 3569 y Fy(x)p Fx(x)p FA(r)1599 3550 y(r)1632 3530 y(r)1665 3511 y(r)1698 3491 y(r)1731 3472 y(r)1764 3452 y(r)1797 3433 y(r)1830 3414 y(r)2174 3445 y Fz(q)2204 3453 y Fl(1)2319 3567 y Fy(&)p Fx(&)2284 3546 y FA(L)2251 3527 y(L)2218 3508 y(L)2185 3489 y(L)2152 3469 y(L)2119 3450 y(L)2086 3431 y(L)2054 3412 y(L)2021 3392 y(L)1968 3225 y Fz(w)1943 3123 y Fy(O)p Fx(O)p 1941 3273 4 150 v 1431 3637 a FB(E)1493 3607 y Fz(S)1229 3706 y(d)1264 3681 y Fp(S)1264 3723 y Fl(0)1207 3833 y Fy({)p Fx({)p FA(x)1238 3809 y(x)1269 3784 y(x)1301 3760 y(x)1332 3736 y(x)1363 3711 y(x)1395 3687 y(x)1713 3706 y Fz(d)1748 3681 y Fp(S)1748 3723 y Fl(1)1878 3842 y Fy(&)p Fx(&)1842 3821 y FA(M)1808 3801 y(M)1773 3781 y(M)1738 3761 y(M)1704 3741 y(M)1669 3721 y(M)1635 3701 y(M)1600 3682 y(M)1565 3662 y(M)1889 3627 y FJ(\000)-11 b(!)2344 3637 y FB(E)2406 3607 y Fz(R)2094 3706 y(d)2129 3681 y Fp(R)2129 3723 y Fl(0)2007 3842 y Fy(x)p Fx(x)p FA(q)2042 3822 y(q)2077 3802 y(q)2112 3782 y(q)2147 3762 y(q)2182 3742 y(q)2217 3722 y(q)2252 3702 y(q)2287 3682 y(q)2586 3706 y Fz(d)2621 3681 y Fp(R)2621 3723 y Fl(1)2685 3828 y Fy(#)p Fx(#)2652 3803 y FA(G)2620 3780 y(G)2589 3756 y(G)2558 3732 y(G)2526 3709 y(G)2495 3685 y(G)2463 3662 y(G)1113 3900 y FB(C)735 b(B)d(A)0 4076 y FC(wher)l(e)31 b(the)f(lax)g(c)l(ommutative)h(squar)l (e)f(in)g(the)g(midd)t(le)i(is)f(a)f(pul)t(lb)l(ack)i(squar)l(e)e (\(henc)l(e)g(the)h(c)l(omp)l(arison)g(is)g(the)f(identity\),)0 4176 y(and)g FF(w)i FC(is)d(a)h(map,)h(surje)l(ctive)e(on)h(obje)l (cts,)g(c)l(oming)g(fr)l(om)g(c)l(omp)l(osing)h FB(E)2343 4146 y Fz(S)2420 4176 y FC(and)f FB(E)2643 4146 y Fz(R)2727 4176 y FC(as)f(\014br)l(ations.)39 b(Then)30 b(the)f(squar)l(e)h(is)0 4275 y(exact)g(and)g FF(w)i FC(is)e(an)g(absolutely)h(dense)f(monotone) g(map.)125 4440 y FL(In)d(the)g(extension)f(theorem)f(w)n(e)i(will)d (demand)j(that)g(a)g(certain)e(functor)i FF(T)34 b FL(:)23 b FI(Pre)h FK(\000)-15 b(!)24 b FI(Pre)j FL(preserv)n(es)e(exact)i (squares,)0 4539 y(whereas)f(the)h(pro)r(of)g(of)g(the)g(theorem)f (actually)e(only)i(needs)h(the)g(at)g(\014rst)g(sigh)n(t)e(w)n(eak)n (er)g(requiremen)n(t)g(that)i FF(T)38 b FL(preserv)n(es)0 4639 y(strict)33 b(exact)h(squares)e(and)i(preserv)n(es)e(the)i (exactness)g(of)g(comma)d(squares)i(of)h(the)g(form)f(1)2994 4651 y Ft(A)3063 4639 y FF(=)p FL(1)3147 4651 y Ft(A)3250 4639 y FL(\(the)i(former)d(b)r(eing)0 4739 y(needed)h(for)f(preserv)-5 b(ation)30 b(of)i(comp)r(osition)d(and)j(the)h(latter)e(for)h(preserv) -5 b(ation)30 b(of)j(iden)n(tities\).)49 b(It)33 b(therefore)e(seems)g (of)0 4838 y(in)n(terest)26 b(to)i(presen)n(t)f(the)h(follo)n(wing)23 b(result.)0 4987 y FM(Prop)s(osition.)77 b FL(F)-7 b(or)27 b(a)g(lo)r(cally)d(monotone)i FF(T)34 b FL(:)23 b FI(Pre)h FK(\000)-15 b(!)24 b FI(Pre)p FL(,)k(or)e FF(T)34 b FL(:)23 b FI(P)n(os)g FK(\000)-15 b(!)23 b FI(P)n(os)p FL(,)k(the)h(follo)n (wing)c(are)i(equiv)-5 b(alen)n(t:)0 5035 y SDict begin H.S end 0 5035 a 0 5035 a SDict begin 12 H.A end 0 5035 a 0 5035 a SDict begin [/View [/XYZ H.V]/Dest (Item.34) cvn /DEST pdfmark end 0 5035 a Black 101 5151 a FL(1.)p Black 42 w FF(T)38 b FL(preserv)n(es)26 b FC(lax)38 b FL(exact)27 b(squares.)p Black 1908 5400 a(14)p Black eop end end %%Page: 15 15 TeXDict begin HPSdict begin 15 14 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.15) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.35) cvn /DEST pdfmark end 0 0 a Black 101 83 a FL(2.)p Black 42 w FF(T)38 b FL(preserv)n(es)26 b(strict)g(exact)h(squares)f (and)i(exactness)e(of)i(comma)d(squares)h(of)i(the)g(form)e(1)3062 95 y Ft(A)3131 83 y FF(=)p FL(1)3215 95 y Ft(A)3284 83 y FL(,)i(for)f(all)e FB(A)19 b FL(.)0 137 y SDict begin H.S end 0 137 a 0 137 a SDict begin 12 H.A end 0 137 a 0 137 a SDict begin [/View [/XYZ H.V]/Dest (Item.36) cvn /DEST pdfmark end 0 137 a Black 101 249 a FL(3.)p Black 42 w FF(T)48 b FL(preserv)n(es)36 b(strict)g(exact)h(squares)f (and)i(exactness)e(of)i(comma)d(squares)h(of)h(the)h(form)f FF(f)9 b(=)p FL(1)3284 261 y Ft(B)3347 249 y FL(,)40 b(1)3452 261 y Ft(A)3521 249 y FF(=f)9 b FL(,)39 b(for)e(all)208 349 y FF(f)31 b FL(:)23 b FB(A)42 b FK(\000)-14 b(!)23 b FB(B)s FL(.)0 398 y SDict begin H.S end 0 398 a 0 398 a SDict begin 12 H.A end 0 398 a 0 398 a SDict begin [/View [/XYZ H.V]/Dest (Item.37) cvn /DEST pdfmark end 0 398 a Black 101 515 a FL(4.)p Black 42 w FF(T)38 b FL(preserv)n(es)26 b(strict)g(exact)h(squares)f(and)i(exactness)e(of)i (comma)d(squares.)p Black 0 681 a FC(Pr)l(o)l(of.)p Black 43 w FL(\(1\))j(implies)c(\(2\):)37 b(clear.)0 830 y(\(2\))e(implies)c (\(3\):)51 b(Supp)r(ose)35 b FF(f)43 b FL(:)35 b FB(A)53 b FK(\000)-14 b(!)35 b FB(B)j FL(is)c(a)g(monotone)f(map.)57 b(W)-7 b(e)35 b(pro)n(v)n(e)e(that)i FF(T)46 b FL(preserv)n(es)32 b(exactness)i(of)h(the)0 930 y(comma)25 b(square)1855 1041 y FF(f)9 b(=)p FL(1)1989 1053 y Ft(B)1673 1147 y Fz(\031)1712 1155 y Fl(0)1631 1285 y Fy(|)p Fx(|)p FA(y)1661 1260 y(y)1691 1236 y(y)1720 1211 y(y)1750 1187 y(y)1780 1162 y(y)1810 1138 y(y)1840 1113 y(y)2161 1147 y Fz(\031)2200 1155 y Fl(1)2276 1287 y Fy(")p Fx(")2244 1261 y FA(E)2214 1236 y(E)2184 1211 y(E)2154 1186 y(E)2124 1162 y(E)2094 1137 y(E)2064 1112 y(E)2034 1087 y(E)1520 1361 y FB(A)1704 1559 y Fz(f)1889 1597 y Fy(")p Fx(")1856 1571 y FA(F)1827 1548 y(F)1798 1525 y(F)1768 1502 y(F)1739 1479 y(F)1709 1455 y(F)1680 1432 y(F)1650 1409 y(F)1621 1386 y(F)1900 1352 y FJ(\000)-11 b(!)2301 1361 y FB(B)2158 1556 y FE(1)2191 1565 y Fo(B)2018 1596 y Fy(|)p Fx(|)p FA(x)2047 1573 y(x)2076 1550 y(x)2105 1527 y(x)2134 1504 y(x)2163 1481 y(x)2192 1458 y(x)2221 1435 y(x)2250 1412 y(x)1914 1668 y FB(B)0 1814 y FL(That)28 b FF(T)38 b FL(preserv)n(es)26 b(exactness)g(of)i(comma)d(squares)h(of)i(the)g(form)e(1)2170 1826 y Ft(A)2239 1814 y FF(=f)36 b FL(is)26 b(pro)n(v)n(ed)g (analogously)-7 b(.)125 1913 y(De\014ne)28 b FF(e)22 b FL(:)i FB(P)29 b FK(\000)-14 b(!)23 b FF(f)9 b(=)p FL(1)894 1925 y Ft(B)985 1913 y FL(b)n(y)27 b(the)h(univ)n(ersal)c (prop)r(ert)n(y)j(in)537 2727 y SDict begin H.S end 537 2727 a 950 2262 a FB(P)1020 2413 y Fz(e)995 2494 y Fy(\017)p Fx(\017)p 993 2494 4 208 v 896 2582 a FF(f)9 b(=)p FL(1)1030 2594 y Ft(B)715 2687 y Fz(\031)754 2695 y Fl(0)672 2825 y Fy(|)p Fx(|)p FA(y)702 2800 y(y)732 2776 y(y)762 2751 y(y)792 2727 y(y)822 2702 y(y)852 2678 y(y)882 2653 y(y)1203 2687 y Fz(\031)1242 2695 y Fl(1)1318 2827 y Fy(")p Fx(")1285 2801 y FA(E)1255 2776 y(E)1225 2751 y(E)1195 2726 y(E)1165 2702 y(E)1135 2677 y(E)1105 2652 y(E)1075 2627 y(E)562 2901 y FB(A)745 3099 y Fz(f)931 3137 y Fy(")p Fx(")898 3111 y FA(F)869 3088 y(F)839 3065 y(F)810 3042 y(F)780 3019 y(F)751 2996 y(F)721 2972 y(F)692 2949 y(F)663 2926 y(F)942 2892 y FJ(\000)-12 b(!)1343 2901 y FB(B)1199 3096 y FE(1)1232 3105 y Fo(B)1059 3137 y Fy(|)p Fx(|)1059 3136 y FA(x)1088 3113 y(x)1117 3090 y(x)1146 3067 y(x)1175 3044 y(x)1205 3021 y(x)1234 2998 y(x)1263 2975 y(x)1292 2952 y(x)956 3208 y FB(B)1552 2727 y FL(=)2417 2108 y FB(P)2208 2206 y Fz(s)2239 2181 y Fq(0)2239 2222 y Fl(1)2191 2345 y Fy(~)p Fx(~)p FA(})2219 2318 y(})2246 2292 y(})2274 2266 y(})2301 2240 y(})2329 2214 y(})2357 2188 y(})2384 2162 y(})2684 2206 y Fz(s)2715 2181 y Fq(0)2715 2222 y Fl(0)2796 2341 y Fy(#)p Fx(#)2763 2316 y FA(G)2733 2293 y(G)2703 2270 y(G)2673 2247 y(G)2643 2224 y(G)2613 2202 y(G)2583 2179 y(G)2553 2156 y(G)2523 2133 y(G)2083 2428 y FB(A)1845 2533 y FE(1)1878 2542 y Fo(A)1856 2665 y Fy(~)p Fx(~)p FA(~)1883 2639 y(~)1911 2613 y(~)1938 2586 y(~)1966 2560 y(~)1993 2534 y(~)2020 2508 y(~)2048 2482 y(~)2317 2531 y Fz(f)2398 2666 y Fy( )p Fx( )2368 2637 y FA(A)2340 2611 y(A)2313 2585 y(A)2285 2558 y(A)2257 2532 y(A)2229 2506 y(A)2201 2479 y(A)2174 2453 y(A)2425 2368 y FE(\()p Fz(i)p FE(\))2757 2428 y FL(1)2799 2440 y Ft(B)2863 2428 y FF(=)p FL(1)2947 2440 y Ft(B)2598 2534 y Fz(s)2629 2542 y Fl(1)2527 2678 y Fy({)p Fx({)p FA(w)2556 2655 y(w)2586 2633 y(w)2615 2611 y(w)2645 2588 y(w)2675 2566 y(w)2704 2543 y(w)2734 2521 y(w)2763 2498 y(w)3103 2525 y Fz(p)3137 2500 y Fq(0)3137 2542 y Fl(1)3235 2677 y Fy(#)p Fx(#)3202 2652 y FA(F)3173 2630 y(F)3144 2608 y(F)3115 2585 y(F)3086 2563 y(F)3057 2541 y(F)3028 2518 y(F)2999 2496 y(F)2970 2474 y(F)1748 2748 y FB(A)1898 2946 y Fz(f)2061 2975 y Fy( )p Fx( )2030 2947 y FA(B)2003 2922 y(B)1976 2897 y(B)1949 2872 y(B)1922 2847 y(B)1895 2822 y(B)1868 2797 y(B)1840 2772 y(B)2079 2687 y FE(\()p Fz(ii)p FE(\))2423 2748 y FB(B)2187 2846 y FE(1)2220 2855 y Fo(B)2190 2975 y Fy(~)p Fx(~)p FA(|)2217 2950 y(|)2245 2925 y(|)2272 2900 y(|)2299 2875 y(|)2327 2850 y(|)2354 2825 y(|)2382 2800 y(|)2679 2846 y FE(1)2712 2855 y Fo(B)2820 2987 y Fy(#)p Fx(#)2786 2963 y FA(H)2753 2939 y(H)2721 2915 y(H)2688 2891 y(H)2656 2868 y(H)2623 2844 y(H)2590 2820 y(H)2558 2796 y(H)2525 2772 y(H)2820 2687 y FE(\()p Fz(iii)p FE(\))2827 2738 y FJ(\000)h(!)3260 2748 y FB(B)3098 2943 y FE(1)3131 2952 y Fo(B)2948 2986 y Fy({)p Fx({)2948 2987 y FA(w)2980 2963 y(w)3012 2939 y(w)3044 2916 y(w)3076 2892 y(w)3108 2868 y(w)3140 2845 y(w)3172 2821 y(w)3204 2797 y(w)2086 3055 y FB(B)2187 3250 y FE(1)2220 3259 y Fo(B)2398 3283 y Fy( )p Fx( )2368 3255 y FA(B)2340 3230 y(B)2313 3205 y(B)2285 3180 y(B)2258 3155 y(B)2230 3130 y(B)2203 3105 y(B)2175 3080 y(B)2449 2995 y FE(\()p Fz(iv)r FE(\))2844 3055 y FB(B)2679 3250 y FE(1)2712 3259 y Fo(B)2527 3294 y Fy({)p Fx({)p FA(v)2560 3270 y(v)2592 3246 y(v)2625 3223 y(v)2657 3199 y(v)2690 3175 y(v)2722 3151 y(v)2755 3128 y(v)2787 3104 y(v)2423 3362 y FB(B)3363 2727 y SDict begin 12 H.A end 3363 2727 a 3363 2727 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.6) cvn /DEST pdfmark end 3363 2727 a Black 366 w FL(\(3.6\))p Black 0 3540 a(where)27 b(\()p FF(i)p FL(\),)h(\()p FF(ii)p FL(\),)f(\()p FF(iv)s FL(\))i(are)d(pullbac)n(ks,)f(and)i(\()p FF(iii)p FL(\))h(is)e(a)h (comma)e(square.)125 3640 y(Clearly)-7 b(,)24 b FF(e)f FL(:)g FB(P)30 b FK(\000)-14 b(!)23 b FF(f)9 b(=)p FL(1)942 3652 y Ft(B)1032 3640 y FL(maps)27 b(\()p FF(a;)14 b(b)1399 3610 y FJ(0)1422 3640 y FF(;)g(b)p FL(\))27 b(in)g FB(P)34 b FL(to)28 b(\()p FF(a;)14 b(b)p FL(\))28 b(in)e FF(f)9 b(=)p FL(1)2310 3652 y Ft(B)2401 3640 y FL(and)27 b FF(e)h FL(is)e(a)h(monotone)f(surjection.)125 3740 y(The)21 b(image)e(under)i FF(T)33 b FL(of)21 b(the)h(diagram)c(on)j(the)h(righ) n(t)e(of)h(\()1937 3740 y SDict begin H.S end 1937 3740 a Black FL(3.6)p Black 2044 3686 a SDict begin H.R end 2044 3686 a 2044 3740 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.6) cvn H.B /ANN pdfmark end 2044 3740 a FL(\))h(is)e(exact)h(b)n(y)g(assumptions.)32 b(Hence)22 b(the)g(image)d(under)i FF(T)0 3839 y FL(of)e(the)h(diagram)c(on)i(the) i(left)f(of)g(\()1032 3839 y SDict begin H.S end 1032 3839 a Black FL(3.6)p Black 1139 3786 a SDict begin H.R end 1139 3786 a 1139 3839 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.6) cvn H.B /ANN pdfmark end 1139 3839 a FL(\))g(is)f(exact.)34 b(Since)18 b FF(e)h FL(is)f(a)h(surjection,)h FF(e)2353 3851 y FJ(\005)2392 3839 y FK(\001)r FF(e)2456 3809 y FJ(\005)2517 3839 y FL(=)j(1)2647 3854 y Fz(f)7 b(=)p FE(1)2753 3863 y Fo(B)2811 3839 y FL(.)34 b(Hence)20 b(\()p FF(T)12 b(e)p FL(\))3271 3851 y FJ(\005)3310 3839 y FK(\001)r FL(\()p FF(T)g(e)p FL(\))3499 3809 y FJ(\005)3559 3839 y FL(=)23 b(1)3689 3854 y Fz(T)9 b FE(\()p Fz(f)e(=g)r FE(\))0 3939 y FL(holds)26 b(since)h FF(T)38 b FL(preserv)n(es)26 b(surjections)g(\(express)h(surjectivit)n(y)e(as)i(a)g(strict)f(exact)h (square\).)36 b(Th)n(us)1019 4122 y(\()p FF(T)12 b(\031)1159 4134 y FE(0)1196 4122 y FL(\))1228 4134 y FJ(\005)1284 4122 y FK(\001)19 b FL(\()p FF(T)12 b(\031)1466 4134 y FE(1)1503 4122 y FL(\))1535 4087 y FJ(\005)1656 4122 y FL(=)83 b(\()p FF(T)12 b(\031)1944 4134 y FE(0)1981 4122 y FL(\))2013 4134 y FJ(\005)2070 4122 y FK(\001)18 b FL(\()p FF(T)12 b(e)p FL(\))2275 4134 y FJ(\005)2331 4122 y FK(\001)19 b FL(\()p FF(T)12 b(e)p FL(\))2537 4087 y FJ(\005)2593 4122 y FK(\001)18 b FL(\()p FF(T)12 b(\031)2774 4134 y FE(1)2811 4122 y FL(\))2843 4087 y FJ(\005)1656 4246 y FL(=)83 b(\()p FF(T)12 b(f)d FL(\))1979 4212 y FJ(\005)2035 4246 y FK(\001)18 b FL(\()p FF(T)12 b(g)s FL(\))2244 4258 y FJ(\005)0 4429 y FL(pro)n(ving)25 b(exactness)i(of)1793 4540 y FF(T)12 b FL(\()p FF(f)d(=)p FL(1)2020 4552 y Ft(B)2082 4540 y FL(\))1596 4646 y Fz(T)g(\031)1683 4654 y Fl(0)1565 4777 y Fy(z)p Fx(z)p FA(t)1596 4756 y(t)1628 4735 y(t)1660 4714 y(t)1692 4693 y(t)1723 4672 y(t)1755 4651 y(t)1787 4630 y(t)1818 4609 y(t)2190 4646 y Fz(T)g(\031)2277 4654 y Fl(1)2339 4777 y Fy($)p Fx($)2305 4754 y FA(J)2273 4733 y(J)2242 4712 y(J)2210 4691 y(J)2179 4670 y(J)2147 4649 y(J)2116 4628 y(J)2084 4607 y(J)2053 4586 y(J)1398 4860 y FF(T)j FB(A)1625 5058 y Fz(T)d(f)1859 5086 y Fy(\045)p Fx(\045)1824 5064 y FA(K)1789 5042 y(K)1754 5019 y(K)1718 4997 y(K)1683 4974 y(K)1648 4952 y(K)1613 4930 y(K)1578 4907 y(K)1542 4885 y(K)1900 4850 y FJ(\000)-11 b(!)2363 4860 y FF(T)12 b FB(B)2186 5055 y FE(1)2219 5064 y Fp(T)7 b Fo(B)2048 5086 y Fy(y)p Fx(y)2048 5087 y FA(t)2079 5067 y(t)2110 5047 y(t)2141 5027 y(t)2172 5007 y(t)2203 4987 y(t)2234 4967 y(t)2265 4947 y(t)2296 4928 y(t)2327 4908 y(t)1884 5167 y FF(T)12 b FB(B)p Black 1908 5400 a FL(15)p Black eop end end %%Page: 16 16 TeXDict begin HPSdict begin 16 15 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.16) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a FL(\(3\))28 b(implies)c(\(4\):)37 b(Supp)r(ose)1887 199 y FF(f)9 b(=g)1685 305 y Fz(\031)1724 313 y Fl(0)1662 438 y Fy(})p Fx(})p FA(|)1689 415 y(|)1716 391 y(|)1742 367 y(|)1769 344 y(|)1795 320 y(|)1822 296 y(|)1848 273 y(|)2150 305 y Fz(\031)2189 313 y Fl(1)2244 440 y Fy(!)p Fx(!)2214 413 y FA(B)2187 389 y(B)2160 365 y(B)2134 341 y(B)2107 317 y(B)2080 293 y(B)2054 269 y(B)2027 245 y(B)1552 519 y FB(A)1717 717 y Fz(f)1894 754 y Fy(!)p Fx(!)1862 727 y FA(D)1832 701 y(D)1801 675 y(D)1770 649 y(D)1740 622 y(D)1709 596 y(D)1679 570 y(D)1648 544 y(D)1900 509 y FJ(\000)-11 b(!)2269 519 y FB(B)2150 702 y Fz(g)2013 754 y Fy(})p Fx(})p FA({)2043 728 y({)2074 702 y({)2104 676 y({)2134 650 y({)2164 623 y({)2194 597 y({)2225 571 y({)1919 826 y FB(C)0 970 y FL(is)26 b(a)i(comma)d(square)h(and)h (de\014ne)h FF(e)23 b FL(:)g FB(P)30 b FK(\000)-14 b(!)23 b FF(f)9 b(=g)29 b FL(b)n(y)e(the)h(univ)n(ersal)d(prop)r(ert)n(y)h(in) 550 1780 y SDict begin H.S end 550 1780 a 931 1315 a FB(P)1001 1467 y Fz(e)976 1548 y Fy(\017)p Fx(\017)p 975 1548 4 208 v 909 1635 a FF(f)9 b(=g)707 1741 y Fz(\031)746 1749 y Fl(0)685 1873 y Fy(})p Fx(})685 1874 y FA(|)712 1850 y(|)738 1827 y(|)765 1803 y(|)791 1779 y(|)818 1756 y(|)844 1732 y(|)871 1708 y(|)1173 1741 y Fz(\031)1212 1749 y Fl(1)1267 1876 y Fy(!)p Fx(!)1236 1848 y FA(B)1210 1824 y(B)1183 1800 y(B)1157 1776 y(B)1130 1752 y(B)1103 1728 y(B)1077 1704 y(B)1050 1680 y(B)575 1954 y FB(A)739 2153 y Fz(f)917 2190 y Fy(!)p Fx(!)885 2163 y FA(D)854 2137 y(D)824 2110 y(D)793 2084 y(D)763 2058 y(D)732 2032 y(D)701 2006 y(D)671 1979 y(D)923 1945 y FJ(\000)-12 b(!)1292 1954 y FB(B)1173 2137 y Fz(g)1036 2189 y Fy(})p Fx(})1036 2190 y FA({)1066 2164 y({)1096 2137 y({)1127 2111 y({)1157 2085 y({)1187 2059 y({)1217 2033 y({)1247 2007 y({)942 2262 y FB(C)1502 1780 y FL(=)2473 1162 y FB(P)2245 1259 y Fz(s)2276 1234 y Fq(0)2276 1276 y Fl(1)2209 1394 y Fy(|)p Fx(|)p FA(y)2241 1368 y(y)2272 1342 y(y)2304 1316 y(y)2336 1290 y(y)2367 1264 y(y)2399 1239 y(y)2430 1213 y(y)2727 1259 y Fz(s)2758 1234 y Fq(0)2758 1276 y Fl(0)2825 1394 y Fy(")p Fx(")2793 1367 y FA(E)2761 1342 y(E)2730 1316 y(E)2699 1290 y(E)2667 1264 y(E)2636 1238 y(E)2605 1212 y(E)2574 1186 y(E)2032 1481 y FF(f)9 b(=)p FL(1)2166 1493 y Ft(C)1853 1579 y Fz(p)1887 1554 y Fq(0)1887 1595 y Fl(0)1808 1724 y Fy(|)p Fx(|)p FA(y)1838 1699 y(y)1867 1675 y(y)1897 1651 y(y)1926 1626 y(y)1956 1602 y(y)1986 1577 y(y)2015 1553 y(y)2338 1587 y Fz(s)2369 1595 y Fl(0)2459 1731 y Fy(")p Fx(")2427 1705 y FA(E)2395 1680 y(E)2364 1654 y(E)2333 1629 y(E)2302 1603 y(E)2271 1578 y(E)2240 1552 y(E)2209 1527 y(E)2481 1421 y FE(\()p Fz(i)p FE(\))2813 1481 y FL(1)2855 1493 y Ft(C)2913 1481 y FF(=g)2633 1587 y Fz(s)2664 1595 y Fl(1)2578 1731 y Fy(|)p Fx(|)2578 1730 y FA(y)2609 1705 y(y)2639 1680 y(y)2670 1654 y(y)2701 1629 y(y)2731 1604 y(y)2762 1578 y(y)2793 1553 y(y)3111 1579 y Fz(p)3145 1554 y Fq(0)3145 1595 y Fl(1)3222 1726 y Fy(")p Fx(")3190 1700 y FA(D)3161 1675 y(D)3131 1650 y(D)3102 1626 y(D)3072 1601 y(D)3043 1576 y(D)3014 1552 y(D)2984 1527 y(D)1697 1801 y FB(A)1880 1999 y Fz(f)2068 2040 y Fy(")p Fx(")2036 2014 y FA(F)2006 1991 y(F)1976 1967 y(F)1947 1944 y(F)1917 1920 y(F)1887 1896 y(F)1857 1873 y(F)1828 1849 y(F)1798 1826 y(F)2084 1741 y FE(\()p Fz(ii)p FE(\))2080 1791 y FJ(\000)-11 b(!)2484 1801 y FB(C)2228 1900 y FE(1)2261 1909 y Fo(C)2188 2040 y Fy(|)p Fx(|)p FA(x)2218 2017 y(x)2248 1993 y(x)2278 1969 y(x)2308 1946 y(x)2338 1922 y(x)2368 1899 y(x)2398 1875 y(x)2428 1851 y(x)2723 1900 y FE(1)2756 1909 y Fo(C)2846 2040 y Fy(")p Fx(")2813 2014 y FA(F)2783 1991 y(F)2754 1967 y(F)2724 1943 y(F)2694 1920 y(F)2665 1896 y(F)2635 1873 y(F)2605 1849 y(F)2576 1826 y(F)2839 1741 y FE(\()p Fz(iii)p FE(\))2846 1791 y FJ(\000)g(!)3247 1801 y FB(B)3112 1984 y Fz(g)2965 2039 y Fy(|)p Fx(|)p FA(y)2994 2016 y(y)3023 1993 y(y)3052 1969 y(y)3081 1946 y(y)3110 1922 y(y)3139 1899 y(y)3168 1875 y(y)3197 1852 y(y)2093 2108 y FB(C)2228 2303 y FE(1)2261 2312 y Fo(C)2459 2348 y Fy(")p Fx(")2426 2322 y FA(F)2396 2298 y(F)2366 2275 y(F)2336 2251 y(F)2306 2227 y(F)2276 2204 y(F)2246 2180 y(F)2216 2157 y(F)2186 2133 y(F)2461 2048 y FE(\()p Fz(iv)r FE(\))2870 2108 y FB(C)2723 2303 y FE(1)2756 2312 y Fo(C)2578 2347 y Fy(|)p Fx(|)p FA(x)2608 2323 y(x)2637 2300 y(x)2667 2276 y(x)2696 2253 y(x)2726 2229 y(x)2756 2206 y(x)2785 2182 y(x)2815 2158 y(x)2484 2415 y FB(C)3350 1780 y SDict begin 12 H.A end 3350 1780 a 3350 1780 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.7) cvn /DEST pdfmark end 3350 1780 a Black 379 w FL(\(3.7\))p Black 0 2591 a(where)27 b(\()p FF(i)p FL(\))h(and)f(\()p FF(iv)s FL(\))h(are)f(pullbac)n(ks,)e (\()p FF(ii)p FL(\))i(and)h(\()p FF(iii)p FL(\))f(are)f(comma)f (squares.)125 2690 y(Clearly)-7 b(,)24 b FF(e)f FL(:)g FB(P)30 b FK(\000)-14 b(!)23 b FF(f)9 b(=g)29 b FL(maps)d(\()p FF(a;)14 b(c;)g(b)p FL(\))28 b(in)f FB(P)34 b FL(to)28 b(\()p FF(a;)14 b(b)p FL(\))27 b(in)g FF(f)9 b(=g)29 b FL(and)f FF(e)f FL(is)g(a)g(monotone)f(surjection.)125 2790 y(The)21 b(image)e(under)i FF(T)33 b FL(of)21 b(the)h(diagram)c (on)j(the)h(righ)n(t)e(of)h(\()1937 2790 y SDict begin H.S end 1937 2790 a Black FL(3.7)p Black 2044 2736 a SDict begin H.R end 2044 2736 a 2044 2790 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.7) cvn H.B /ANN pdfmark end 2044 2790 a FL(\))h(is)e(exact)h(b)n(y)g(assumptions.)32 b(Hence)22 b(the)g(image)d(under)i FF(T)0 2890 y FL(of)g(the)h(diagram) c(on)k(the)g(left)f(of)g(\()1048 2890 y SDict begin H.S end 1048 2890 a Black FL(3.7)p Black 1155 2836 a SDict begin H.R end 1155 2836 a 1155 2890 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.7) cvn H.B /ANN pdfmark end 1155 2890 a FL(\))g(is)g(exact.)34 b(Since)21 b FF(e)g FL(is)g(a)g (surjection,)g FF(e)2385 2902 y FJ(\005)2429 2890 y FK(\001)6 b FF(e)2497 2859 y FJ(\005)2558 2890 y FL(=)23 b(1)2688 2905 y Fz(f)7 b(=g)2799 2890 y FL(.)35 b(Hence)22 b(\()p FF(T)12 b(e)p FL(\))3262 2902 y FJ(\005)3305 2890 y FK(\001)6 b FL(\()p FF(T)12 b(e)p FL(\))3498 2859 y FJ(\005)3559 2890 y FL(=)23 b(1)3689 2905 y Fz(T)9 b FE(\()p Fz(f)e(=g)r FE(\))0 2989 y FL(holds)26 b(since)h FF(T)38 b FL(preserv)n(es)26 b(surjections)g(\(express)h(surjectivit)n(y)e(as)i(a)g(strict)f(exact)h (square\).)36 b(Th)n(us)1019 3169 y(\()p FF(T)12 b(\031)1159 3181 y FE(0)1196 3169 y FL(\))1228 3181 y FJ(\005)1284 3169 y FK(\001)19 b FL(\()p FF(T)12 b(\031)1466 3181 y FE(1)1503 3169 y FL(\))1535 3134 y FJ(\005)1656 3169 y FL(=)83 b(\()p FF(T)12 b(\031)1944 3181 y FE(0)1981 3169 y FL(\))2013 3181 y FJ(\005)2070 3169 y FK(\001)18 b FL(\()p FF(T)12 b(e)p FL(\))2275 3181 y FJ(\005)2331 3169 y FK(\001)19 b FL(\()p FF(T)12 b(e)p FL(\))2537 3134 y FJ(\005)2593 3169 y FK(\001)18 b FL(\()p FF(T)12 b(\031)2774 3181 y FE(1)2811 3169 y FL(\))2843 3134 y FJ(\005)1656 3293 y FL(=)83 b(\()p FF(T)12 b(f)d FL(\))1979 3259 y FJ(\005)2035 3293 y FK(\001)18 b FL(\()p FF(T)12 b(g)s FL(\))2244 3305 y FJ(\005)0 3473 y FL(pro)n(ving)25 b(exactness)i(of)1824 3585 y FF(T)12 b FL(\()p FF(f)d(=g)s FL(\))1608 3690 y Fz(T)g(\031)1695 3698 y Fl(0)1590 3821 y Fy(z)p Fx(z)p FA(v)1624 3798 y(v)1658 3774 y(v)1691 3750 y(v)1725 3726 y(v)1759 3702 y(v)1792 3678 y(v)1826 3654 y(v)2178 3690 y Fz(T)g(\031)2265 3698 y Fl(1)2314 3821 y Fy($)p Fx($)2280 3797 y FA(H)2247 3773 y(H)2213 3749 y(H)2180 3726 y(H)2147 3702 y(H)2113 3678 y(H)2080 3654 y(H)2046 3630 y(H)1430 3904 y FF(T)j FB(A)1638 4102 y Fz(T)d(f)1864 4130 y Fy($)p Fx($)1830 4106 y FA(I)1797 4084 y(I)1765 4062 y(I)1732 4040 y(I)1700 4018 y(I)1667 3996 y(I)1634 3973 y(I)1602 3951 y(I)1569 3929 y(I)1900 3895 y FJ(\000)-11 b(!)2332 3904 y FF(T)12 b FB(B)2181 4102 y Fz(T)d(g)2043 4129 y Fy(z)p Fx(z)p FA(u)2075 4107 y(u)2107 4085 y(u)2140 4063 y(u)2172 4041 y(u)2204 4019 y(u)2236 3997 y(u)2268 3975 y(u)2300 3953 y(u)1889 4211 y FF(T)j FB(C)0 4403 y FL(\(4\))28 b(implies)c(\(1\):)37 b(Supp)r(ose)27 b(that)h(the)g(lax)e(square)1754 4619 y FB(P)1936 4562 y Fz(p)1970 4570 y Fl(1)2069 4599 y Fy(/)p Fx(/)p 1869 4600 200 4 v 1708 4759 a Fz(p)1742 4767 y Fl(0)1799 4843 y Fy(\017)p Fx(\017)p 1798 4843 4 200 v 2094 4619 a FB(B)2158 4751 y Fz(g)2133 4843 y Fy(\017)p Fx(\017)p 2131 4843 V 1756 4926 a FB(A)1951 4971 y Fz(f)2073 4906 y Fy(/)p Fx(/)p 1867 4907 207 4 v 1933 4767 a FJ(\045)2098 4926 y FB(C)0 5151 y FL(is)g(exact.)p Black 1908 5400 a(16)p Black eop end end %%Page: 17 17 TeXDict begin HPSdict begin 17 16 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.17) cvn /DEST pdfmark end -8 -8 a Black Black 125 83 a FL(Observ)n(e)25 b(that)j(there)g(is)e(an)i(equalit)n(y)509 882 y SDict begin H.S end 509 882 a 891 417 a FB(S)960 569 y Fz(e)935 649 y Fy(\017)p Fx(\017)p 934 649 4 208 v 869 737 a FF(f)9 b(=g)666 842 y Fz(\031)705 850 y Fl(0)644 975 y Fy(})p Fx(})644 976 y FA(|)671 952 y(|)697 928 y(|)724 905 y(|)750 881 y(|)777 857 y(|)804 834 y(|)830 810 y(|)1132 842 y Fz(\031)1171 850 y Fl(1)1226 978 y Fy(!)p Fx(!)1196 950 y FA(B)1169 926 y(B)1142 902 y(B)1116 878 y(B)1089 854 y(B)1062 830 y(B)1036 806 y(B)1009 782 y(B)534 1056 y FB(A)699 1254 y Fz(f)876 1292 y Fy(!)p Fx(!)844 1265 y FA(D)813 1238 y(D)783 1212 y(D)752 1186 y(D)722 1160 y(D)691 1134 y(D)660 1107 y(D)630 1081 y(D)882 1047 y FJ(\000)-11 b(!)1251 1056 y FB(B)1132 1239 y Fz(g)995 1291 y Fy(})p Fx(})p FA({)1025 1265 y({)1055 1239 y({)1086 1213 y({)1116 1187 y({)1146 1161 y({)1176 1135 y({)1207 1108 y({)901 1363 y FB(C)1461 882 y FL(=)2474 263 y FB(S)2236 361 y Fz(s)2267 336 y Fq(0)2267 378 y Fl(1)2192 496 y Fy({)p Fx({)p FA(x)2222 473 y(x)2251 450 y(x)2280 428 y(x)2309 405 y(x)2339 382 y(x)2368 359 y(x)2397 337 y(x)2426 314 y(x)2734 361 y Fz(s)2765 336 y Fq(0)2765 378 y Fl(0)2841 496 y Fy(")p Fx(")2808 470 y FA(F)2779 447 y(F)2750 425 y(F)2721 402 y(F)2692 379 y(F)2663 356 y(F)2634 334 y(F)2605 311 y(F)2576 288 y(F)1991 583 y FL(1)2033 595 y Ft(A)2103 583 y FF(=p)2187 595 y FE(0)1824 681 y Fz(p)1858 655 y Fq(0)1858 697 y Fl(0)1767 829 y Fy(|)p Fx(|)p FA(x)1799 804 y(x)1831 779 y(x)1863 754 y(x)1894 729 y(x)1926 704 y(x)1958 679 y(x)1990 654 y(x)2325 689 y Fz(s)2356 697 y Fl(0)2447 827 y Fy(#)p Fx(#)2415 802 y FA(F)2383 777 y(F)2351 752 y(F)2319 728 y(F)2288 703 y(F)2256 678 y(F)2224 653 y(F)2192 629 y(F)2480 523 y FE(\()p Fz(i)p FE(\))2812 583 y FF(p)2854 595 y FE(1)2891 583 y FF(=)p FL(1)2975 595 y Ft(B)2645 689 y Fz(s)2676 697 y Fl(1)2588 827 y Fy(|)p Fx(|)p FA(x)2619 802 y(x)2651 777 y(x)2682 753 y(x)2714 728 y(x)2745 703 y(x)2776 679 y(x)2808 654 y(x)3139 681 y Fz(p)3173 655 y Fq(0)3173 697 y Fl(1)3263 831 y Fy(")p Fx(")3230 805 y FA(F)3198 780 y(F)3167 754 y(F)3135 729 y(F)3103 704 y(F)3072 679 y(F)3040 654 y(F)3009 629 y(F)1657 903 y FB(A)1805 1098 y FE(1)1838 1107 y Fo(A)2039 1138 y Fy(#)p Fx(#)2006 1113 y FA(G)1975 1090 y(G)1945 1067 y(G)1914 1044 y(G)1883 1020 y(G)1852 997 y(G)1821 974 y(G)1791 951 y(G)1760 928 y(G)2058 842 y FE(\()p Fz(ii)p FE(\))2054 893 y FJ(\000)f(!)2472 903 y FB(P)2235 999 y Fz(p)2269 1007 y Fl(0)2175 1138 y Fy({)p Fx({)p FA(w)2206 1115 y(w)2237 1092 y(w)2268 1069 y(w)2299 1045 y(w)2330 1022 y(w)2361 999 y(w)2392 976 y(w)2423 952 y(w)2732 999 y Fz(p)2766 1007 y Fl(1)2861 1141 y Fy(#)p Fx(#)2828 1116 y FA(G)2797 1092 y(G)2765 1069 y(G)2734 1045 y(G)2703 1022 y(G)2672 998 y(G)2640 975 y(G)2609 951 y(G)2578 928 y(G)2864 842 y FE(\()p Fz(iii)p FE(\))2872 893 y FJ(\000)g(!)3287 903 y FB(B)3135 1098 y FE(1)3168 1107 y Fo(B)2989 1140 y Fy({)p Fx({)2989 1139 y FA(w)3020 1116 y(w)3051 1093 y(w)3081 1069 y(w)3112 1046 y(w)3142 1023 y(w)3173 999 y(w)3203 976 y(w)3234 952 y(w)2064 1210 y FB(A)2260 1408 y Fz(f)2458 1452 y Fy(#)p Fx(#)2425 1427 y FA(G)2393 1403 y(G)2361 1379 y(G)2329 1355 y(G)2296 1331 y(G)2264 1307 y(G)2232 1283 y(G)2200 1259 y(G)2168 1235 y(G)2463 1150 y FE(\()p Fz(iv)r FE(\))2465 1200 y FJ(\000)g(!)2886 1210 y FB(B)2736 1393 y Fz(g)2577 1451 y Fy({)p Fx({)p FA(w)2609 1427 y(w)2641 1403 y(w)2672 1379 y(w)2704 1355 y(w)2736 1331 y(w)2768 1308 y(w)2800 1284 y(w)2831 1260 y(w)2483 1517 y FB(C)3391 882 y SDict begin 12 H.A end 3391 882 a 3391 882 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.8) cvn /DEST pdfmark end 3391 882 a Black 338 w FL(\(3.8\))p Black 0 1685 a(where)34 b(the)i(diagrams)31 b(on)j(the)i(righ)n(t)d (are:)51 b(\()p FF(i)p FL(\))35 b(is)e(a)i(pullbac)n(k,)f(\()p FF(ii)p FL(\))h(and)g(\()p FF(iii)p FL(\))f(are)g(comma)e(ob)5 b(jects,)37 b(and)d(\()p FF(iv)s FL(\))i(is)e(the)0 1785 y(original)28 b(lax)j(exact)h(square.)51 b(On)32 b(the)h(left,)h(the)f (morphism)c FF(e)i FL(:)g FB(S)48 b FK(\000)-15 b(!)32 b FF(f)9 b(=g)34 b FL(is)e(induced)g(b)n(y)g(the)h(univ)n(ersal)c(prop) r(ert)n(y)0 1885 y(of)g(comma)d(squares.)38 b(Observ)n(e)27 b(that)i FF(e)f FL(is)g(a)g(monotone)f(surjection:)37 b FF(e)28 b FL(maps)g(\()p FF(a;)14 b(w)r(;)g(b)p FL(\))29 b(in)f FB(S)44 b FL(to)29 b(\()p FF(a;)14 b(b)p FL(\))29 b(in)e FF(f)9 b(=g)s FL(,)28 b(and)h(for)0 1984 y(\()p FF(a;)14 b(b)p FL(\))28 b(in)f FF(f)9 b(=g)29 b FL(there)e(is)g(\()p FF(a;)14 b(w)r(;)g(b)p FL(\))28 b(in)f FB(S)43 b FL(b)n(y)28 b(exactness.)125 2084 y(Therefore,)e(the)i(diagram)1454 2264 y FB(S)1523 2416 y Fz(e)1498 2497 y Fy(\017)p Fx(\017)p 1496 2497 4 208 v 1431 2584 a FF(f)9 b(=g)1229 2690 y Fz(\031)1268 2698 y Fl(0)1207 2822 y Fy(})p Fx(})1207 2823 y FA(|)1233 2799 y(|)1260 2776 y(|)1287 2752 y(|)1313 2728 y(|)1340 2705 y(|)1366 2681 y(|)1393 2657 y(|)1694 2690 y Fz(\031)1733 2698 y Fl(1)1789 2825 y Fy(!)p Fx(!)1758 2797 y FA(B)1732 2773 y(B)1705 2749 y(B)1678 2725 y(B)1652 2701 y(B)1625 2677 y(B)1598 2653 y(B)1572 2629 y(B)1096 2903 y FB(A)1261 3102 y Fz(f)1438 3139 y Fy(!)p Fx(!)1407 3112 y FA(D)1376 3086 y(D)1345 3059 y(D)1315 3033 y(D)1284 3007 y(D)1254 2981 y(D)1223 2955 y(D)1193 2928 y(D)1445 2894 y FJ(\000)-12 b(!)1814 2903 y FB(B)1695 3086 y Fz(g)1558 3138 y Fy(})p Fx(})1558 3139 y FA({)1588 3113 y({)1618 3086 y({)1648 3060 y({)1678 3034 y({)1709 3008 y({)1739 2982 y({)1769 2956 y({)1463 3211 y FB(C)1941 2729 y FL(=)2388 2430 y FB(S)2124 2530 y Fz(\031)2163 2538 y Fl(0)2195 2530 y FJ(\001)p Fz(e)2164 2655 y Fy(~)p Fx(~)2164 2654 y FA(|)2190 2630 y(|)2217 2605 y(|)2244 2581 y(|)2271 2556 y(|)2298 2532 y(|)2324 2507 y(|)2351 2483 y(|)2616 2530 y Fz(\031)2655 2538 y Fl(1)2688 2530 y FJ(\001)p Fz(e)2700 2657 y Fy( )p Fx( )2670 2629 y FA(A)2643 2604 y(A)2616 2580 y(A)2589 2555 y(A)2562 2530 y(A)2535 2505 y(A)2508 2480 y(A)2481 2455 y(A)2053 2737 y FB(A)2204 2936 y Fz(f)2372 2969 y Fy( )p Fx( )2341 2941 y FA(B)2314 2916 y(B)2286 2890 y(B)2258 2865 y(B)2230 2839 y(B)2202 2813 y(B)2174 2788 y(B)2146 2762 y(B)2378 2728 y FJ(\000)h(!)2725 2737 y FB(B)2620 2920 y Fz(g)2491 2969 y Fy(~)p Fx(~)p FA(})2519 2944 y(})2547 2918 y(})2574 2893 y(})2602 2867 y(})2629 2842 y(})2657 2816 y(})2685 2791 y(})2397 3045 y FB(C)0 3374 y FL(is)26 b(exact,)i(i.e.,)e(the)i(equalit)n(y)1428 3474 y(\()p FF(\031)1507 3486 y FE(0)1545 3474 y FL(\))1577 3486 y FJ(\005)1634 3474 y FK(\001)18 b FF(e)1714 3486 y FJ(\005)1770 3474 y FK(\001)h FF(e)1851 3440 y FJ(\005)1907 3474 y FK(\001)g FL(\()p FF(\031)2028 3486 y FE(1)2066 3474 y FL(\))2098 3440 y FJ(\005)2159 3474 y FL(=)k FF(f)2297 3440 y FJ(\005)2353 3474 y FK(\001)18 b FF(g)2434 3486 y FJ(\005)0 3617 y FL(holds.)35 b(This)25 b(follo)n(ws)d(from)j FF(e)941 3629 y FJ(\005)993 3617 y FK(\001)15 b FF(e)1070 3587 y FJ(\005)1131 3617 y FL(=)22 b(1)1260 3632 y Fz(f)7 b(=g)1371 3617 y FL(,)26 b(since)f FF(e)g FL(is)g(surjectiv)n(e)f(and)h (from)g(the)h(fact)g(that)g(comma)d(squares)h(are)h(exact.)125 3717 y(By)i(assumption,)e(in)i(the)h(diagram)1827 3901 y FF(T)12 b FL(\()p FF(f)d(=g)s FL(\))1574 4005 y Fz(T)g(s)1653 3980 y Fq(0)1653 4022 y Fl(1)1511 4146 y Fy(y)p Fx(y)p FA(r)1544 4126 y(r)1577 4107 y(r)1610 4087 y(r)1644 4067 y(r)1677 4047 y(r)1710 4028 y(r)1743 4008 y(r)1776 3988 y(r)1809 3968 y(r)2226 4005 y Fz(T)g(s)2305 3980 y Fq(0)2305 4022 y Fl(0)2399 4146 y Fy(\045)p Fx(\045)2364 4125 y FA(L)2331 4105 y(L)2298 4085 y(L)2265 4066 y(L)2232 4046 y(L)2199 4026 y(L)2166 4006 y(L)2133 3987 y(L)2100 3967 y(L)2067 3947 y(L)1222 4234 y FF(T)j FL(\(1)1357 4246 y Ft(A)1425 4234 y FF(=p)1509 4246 y FE(0)1546 4234 y FL(\))1040 4331 y Fz(T)d(p)1122 4306 y Fq(0)1122 4348 y Fl(0)997 4470 y Fy(y)p Fx(y)p FA(s)1030 4449 y(s)1063 4428 y(s)1096 4406 y(s)1129 4385 y(s)1162 4364 y(s)1195 4343 y(s)1228 4322 y(s)1261 4301 y(s)1668 4339 y Fz(T)g(s)1747 4347 y Fl(0)1856 4475 y Fy(&)p Fx(&)1820 4454 y FA(M)1786 4435 y(M)1752 4415 y(M)1718 4396 y(M)1684 4376 y(M)1651 4357 y(M)1617 4338 y(M)1583 4318 y(M)1549 4299 y(M)1515 4279 y(M)1894 4173 y Fz(T)g FE(\()p Fz(i)p FE(\))2334 4234 y FF(T)j FL(\()p FF(p)2469 4246 y FE(1)2506 4234 y FF(=)p FL(1)2590 4246 y Ft(B)2653 4234 y FL(\))2130 4339 y Fz(T)d(s)2209 4347 y Fl(1)2056 4475 y Fy(x)p Fx(x)2056 4474 y FA(q)2090 4455 y(q)2124 4435 y(q)2157 4416 y(q)2191 4396 y(q)2224 4377 y(q)2258 4358 y(q)2291 4338 y(q)2325 4319 y(q)2359 4300 y(q)2753 4331 y Fz(T)g(p)2835 4306 y Fq(0)2835 4348 y Fl(1)2910 4471 y Fy(\045)p Fx(\045)2875 4449 y FA(J)2842 4428 y(J)2809 4407 y(J)2776 4385 y(J)2744 4364 y(J)2711 4343 y(J)2678 4322 y(J)2645 4300 y(J)2612 4279 y(J)827 4553 y FF(T)j FB(A)1027 4748 y FE(1)1060 4757 y Fp(T)7 b Fo(A)1302 4780 y Fy(\045)p Fx(\045)1267 4758 y FA(K)1234 4738 y(K)1202 4718 y(K)1169 4698 y(K)1137 4678 y(K)1104 4658 y(K)1072 4638 y(K)1039 4618 y(K)1006 4598 y(K)974 4578 y(K)1353 4493 y Fz(T)i FE(\()p Fz(ii)p FE(\))1373 4544 y FJ(\000)-11 b(!)1881 4553 y FF(T)12 b FB(P)1575 4650 y Fz(T)d(p)1657 4658 y Fl(0)1497 4786 y Fy(x)p Fx(x)p FA(q)1531 4767 y(q)1565 4749 y(q)1599 4730 y(q)1633 4711 y(q)1667 4692 y(q)1701 4673 y(q)1735 4655 y(q)1769 4636 y(q)1803 4617 y(q)1837 4598 y(q)2221 4650 y Fz(T)g(p)2303 4658 y Fl(1)2416 4787 y Fy(&)p Fx(&)2379 4767 y FA(M)2345 4748 y(M)2311 4729 y(M)2277 4711 y(M)2243 4692 y(M)2209 4673 y(M)2175 4654 y(M)2141 4635 y(M)2107 4616 y(M)2073 4597 y(M)2038 4578 y(M)2398 4493 y Fz(T)g FE(\()p Fz(iii)p FE(\))2430 4544 y FJ(\000)-12 b(!)2934 4553 y FF(T)12 b FB(B)2748 4748 y FE(1)2781 4757 y Fp(T)7 b Fo(B)2604 4781 y Fy(y)p Fx(y)p FA(s)2637 4761 y(s)2669 4741 y(s)2701 4721 y(s)2734 4701 y(s)2766 4681 y(s)2798 4660 y(s)2831 4640 y(s)2863 4620 y(s)2895 4600 y(s)1327 4860 y FF(T)12 b FB(A)1597 5058 y Fz(T)d(f)1867 5097 y Fy(&)p Fx(&)1830 5077 y FA(M)1796 5058 y(M)1761 5039 y(M)1726 5020 y(M)1691 5001 y(M)1656 4981 y(M)1622 4962 y(M)1587 4943 y(M)1552 4924 y(M)1517 4904 y(M)1482 4885 y(M)1877 4800 y Fz(T)g FE(\()p Fz(iv)r FE(\))1903 4851 y FJ(\000)-11 b(!)2440 4860 y FF(T)12 b FB(B)2228 5058 y Fz(T)d(g)2046 5097 y Fy(x)p Fx(x)p FA(q)2080 5078 y(q)2115 5059 y(q)2149 5040 y(q)2184 5021 y(q)2219 5001 y(q)2253 4982 y(q)2288 4963 y(q)2322 4944 y(q)2357 4925 y(q)2391 4906 y(q)1891 5168 y FF(T)j FB(C)p Black 1908 5400 a FL(17)p Black eop end end %%Page: 18 18 TeXDict begin HPSdict begin 18 17 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.18) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a FL(the)33 b(square)f FF(T)12 b FL(\()p FF(i)p FL(\))32 b(is)g(strict)g(exact,)h(and)g FF(T)12 b FL(\()p FF(ii)p FL(\),)33 b FF(T)12 b FL(\()p FF(iii)p FL(\))32 b(are)g(lax)f(exact)h(squares.)52 b(Also,)33 b(the)g(whole)e(diagram)f (is)i(exact,)0 183 y(b)r(eing)27 b(the)h(image)d(of)i(the)h(diagram) 1906 282 y FB(S)1709 396 y Fz(e)1647 515 y Fy(|)p Fx(|)p FA(z)1678 489 y(z)1709 463 y(z)1740 437 y(z)1771 412 y(z)1802 386 y(z)1833 360 y(z)1864 334 y(z)2160 396 y Fz(e)2253 515 y Fy(")p Fx(")2222 488 y FA(D)2191 462 y(D)2160 437 y(D)2129 411 y(D)2098 385 y(D)2067 359 y(D)2036 333 y(D)2005 307 y(D)1500 602 y FF(f)9 b(=g)1614 810 y FE(1)1647 821 y Fp(f)c(=g)1874 847 y Fy(!)p Fx(!)1842 820 y FA(C)1814 795 y(C)1786 771 y(C)1757 746 y(C)1729 721 y(C)1700 697 y(C)1672 672 y(C)1644 648 y(C)2266 602 y FF(f)k(=g)2154 810 y FE(1)2187 821 y Fp(f)c(=g)2027 847 y Fy(})p Fx(})p FA({)2055 822 y({)2083 798 y({)2112 773 y({)2140 749 y({)2168 724 y({)2197 699 y({)2225 675 y({)1883 934 y FF(f)k(=g)1672 1040 y Fz(\031)1711 1048 y Fl(0)1635 1176 y Fy(|)p Fx(|)1635 1177 y FA(z)1664 1152 y(z)1693 1128 y(z)1722 1104 y(z)1751 1079 y(z)1781 1055 y(z)1810 1031 y(z)1839 1006 y(z)2156 1040 y Fz(\031)2195 1048 y Fl(1)2268 1179 y Fy(")p Fx(")2237 1153 y FA(D)2207 1128 y(D)2178 1103 y(D)2148 1079 y(D)2118 1054 y(D)2089 1029 y(D)2059 1004 y(D)2029 980 y(D)1524 1254 y FB(A)1704 1452 y Fz(f)1890 1492 y Fy(")p Fx(")1858 1466 y FA(E)1829 1443 y(E)1800 1419 y(E)1770 1396 y(E)1741 1372 y(E)1712 1349 y(E)1683 1326 y(E)1653 1302 y(E)1624 1279 y(E)1898 1244 y FJ(\000)-11 b(!)2293 1254 y FB(B)2158 1436 y Fz(g)2010 1492 y Fy(|)p Fx(|)2010 1493 y FA(y)2039 1469 y(y)2068 1446 y(y)2097 1422 y(y)2127 1399 y(y)2156 1375 y(y)2185 1352 y(y)2214 1328 y(y)2244 1305 y(y)1915 1561 y FB(C)0 1706 y FL(under)27 b FF(T)39 b FL(\(use)28 b(assumptions:)34 b(the)28 b(upp)r(er)g(square)e(is)h(strict)f(exact,)h(and)h(the)g(lo)n (w)n(er)d(square)h(is)g(a)i(comma)d(ob)5 b(ject\).)125 1806 y(W)-7 b(e)28 b(pro)n(v)n(e)d(that)j FF(T)12 b FL(\()p FF(iv)s FL(\))27 b(is)g(exact.)36 b(Indeed:)1005 1988 y(\()p FF(T)12 b(f)d FL(\))1180 1954 y FJ(\005)1235 1988 y FK(\001)19 b FL(\()p FF(T)12 b(g)s FL(\))1445 2000 y FJ(\005)1565 1988 y FL(=)83 b(\(1)1787 2000 y Fz(T)9 b Ft(A)1905 1988 y FL(\))1937 1954 y FJ(\005)1994 1988 y FK(\001)18 b FL(\()p FF(T)12 b(f)d FL(\))2210 1954 y FJ(\005)2266 1988 y FK(\001)18 b FL(\()p FF(T)12 b(g)s FL(\))2475 2000 y FJ(\005)2531 1988 y FK(\001)19 b FL(\(1)2647 2000 y Fz(T)9 b Ft(B)2759 1988 y FL(\))2791 2000 y FJ(\005)1565 2113 y FL(=)83 b(\()p FF(T)12 b(p)1848 2079 y FJ(0)1848 2133 y FE(0)1884 2113 y FL(\))1916 2125 y FJ(\005)1973 2113 y FK(\001)19 b FL(\()p FF(T)12 b(s)2147 2079 y FJ(0)2147 2133 y FE(1)2183 2113 y FL(\))2215 2125 y FJ(\005)2272 2113 y FK(\001)19 b FL(\()p FF(T)12 b(s)2446 2079 y FJ(0)2446 2133 y FE(0)2482 2113 y FL(\))2514 2079 y FJ(\005)2571 2113 y FK(\001)19 b FL(\()p FF(T)12 b(p)2748 2079 y FJ(0)2748 2133 y FE(1)2784 2113 y FL(\))2816 2079 y FJ(\005)1565 2237 y FL(=)83 b(\()p FF(T)12 b(p)1848 2203 y FJ(0)1848 2258 y FE(0)1884 2237 y FL(\))1916 2249 y FJ(\005)1973 2237 y FK(\001)19 b FL(\()p FF(T)12 b(s)2147 2249 y FE(0)2183 2237 y FL(\))2215 2203 y FJ(\005)2272 2237 y FK(\001)19 b FL(\()p FF(T)12 b(s)2446 2249 y FE(1)2482 2237 y FL(\))2514 2249 y FJ(\005)2571 2237 y FK(\001)19 b FL(\()p FF(T)12 b(p)2748 2203 y FJ(0)2748 2258 y FE(1)2784 2237 y FL(\))2816 2203 y FJ(\005)1565 2362 y FL(=)83 b(\(1)1787 2374 y Fz(T)9 b Ft(A)1905 2362 y FL(\))1937 2328 y FJ(\005)1994 2362 y FK(\001)18 b FL(\()p FF(T)12 b(p)2170 2374 y FE(0)2206 2362 y FL(\))2238 2374 y FJ(\005)2295 2362 y FK(\001)19 b FL(\()p FF(T)12 b(p)2472 2374 y FE(1)2508 2362 y FL(\))2540 2328 y FJ(\005)2597 2362 y FK(\001)19 b FL(\(1)2713 2374 y Fz(T)9 b Ft(B)2825 2362 y FL(\))2857 2374 y FJ(\005)1565 2487 y FL(=)83 b(\()p FF(T)12 b(p)1848 2499 y FE(0)1884 2487 y FL(\))1916 2499 y FJ(\005)1973 2487 y FK(\001)19 b FL(\()p FF(T)12 b(p)2150 2499 y FE(1)2186 2487 y FL(\))2218 2452 y FJ(\005)p 3839 2669 4 57 v 3843 2616 50 4 v 3843 2669 V 3893 2669 4 57 v 0 2794 a SDict begin H.S end 0 2794 a 0 2794 a SDict begin 12 H.A end 0 2794 a 0 2794 a SDict begin [/View [/XYZ H.V]/Dest (section.4) cvn /DEST pdfmark end 0 2794 a 150 x FN(4)135 b(The)44 b(univ)l(ersal)g(prop) t(ert)l(y)h(of)g Fi(\()p Fh(\000)p Fi(\))1941 2962 y FK(\005)2019 2944 y Fi(:)33 b Fg(Pre)g Fh(\000)-19 b(!)32 b Fg(Rel)q Fi(\()p Fg(Pre)p Fi(\))0 3126 y FL(W)-7 b(e)28 b(pro)n(v)n(e)e(no)n(w)h(that)h(the)g(2-functor)e(\()p FK(\000)p FL(\))1349 3138 y FJ(\005)1411 3126 y FL(:)d FI(Pre)g FK(\000)-14 b(!)23 b FI(Rel)o FL(\()p FI(Pre)q FL(\))28 b(has)f(an)g(analogous)d(univ)n(ersal)h(prop)r(ert)n(y)h(to)h (the)h(case)f(of)0 3225 y(sets.)37 b(F)-7 b(rom)26 b(that,)i(the)g (result)e(on)h(a)h(unique)e(lifting)g(of)h FF(T)39 b FL(to)p 1970 3158 61 4 v 27 w FF(T)g FL(will)25 b(immediately)e(follo)n (w,)h(see)k(Theorem)3435 3225 y SDict begin H.S end 3435 3225 a Black FL(5.3)p Black 3542 3172 a SDict begin H.R end 3542 3172 a 3542 3225 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.3) cvn H.B /ANN pdfmark end 3542 3225 a 27 w FL(b)r(elo)n(w.)0 3391 y SDict begin H.S end 0 3391 a 0 3391 a SDict begin 12 H.A end 0 3391 a 0 3391 a SDict begin [/View [/XYZ H.V]/Dest (theorem.4.1) cvn /DEST pdfmark end 0 3391 a Black FM(Theorem)i(4.1.)p Black 40 w FC(The)h(2-functor)f FL(\()p FK(\000)p FL(\))1256 3403 y FJ(\005)1317 3391 y FL(:)23 b FI(Pre)h FK(\000)-14 b(!)23 b FI(Rel)o FL(\()p FI(Pre)q FL(\))30 b FC(has)g(the)g(fol)t (lowing)i(thr)l(e)l(e)e(pr)l(op)l(erties:)0 3445 y SDict begin H.S end 0 3445 a 0 3445 a SDict begin 12 H.A end 0 3445 a 0 3445 a SDict begin [/View [/XYZ H.V]/Dest (Item.38) cvn /DEST pdfmark end 0 3445 a Black 98 3557 a FC(1.)p Black 43 w(Every)g FF(f)486 3569 y FJ(\005)554 3557 y FC(is)g(a)g(left)g(adjoint.)0 3607 y SDict begin H.S end 0 3607 a 0 3607 a SDict begin 12 H.A end 0 3607 a 0 3607 a SDict begin [/View [/XYZ H.V]/Dest (Item.39) cvn /DEST pdfmark end 0 3607 a Black 98 3723 a FC(2.)p Black 43 w(F)-6 b(or)30 b(every)g(exact)g(squar)l(e)g(\()1089 3723 y SDict begin H.S end 1089 3723 a Black FC(3.3)p Black 1199 3670 a SDict begin H.R end 1199 3670 a 1199 3723 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 1199 3723 a FC(\))f(the)h(e)l(quality)h FF(f)1754 3693 y FJ(\005)1810 3723 y FK(\001)18 b FF(g)1891 3735 y FJ(\005)1952 3723 y FL(=)23 b(\()p FF(p)2114 3735 y FE(0)2151 3723 y FL(\))2183 3735 y FJ(\005)2240 3723 y FK(\001)c FL(\()p FF(p)2356 3735 y FE(1)2393 3723 y FL(\))2425 3693 y FJ(\005)2493 3723 y FC(holds.)0 3777 y SDict begin H.S end 0 3777 a 0 3777 a SDict begin 12 H.A end 0 3777 a 0 3777 a SDict begin [/View [/XYZ H.V]/Dest (Item.40) cvn /DEST pdfmark end 0 3777 a Black 98 3889 a FC(3.)p Black 43 w(F)-6 b(or)33 b(every)h(absolutely)h(dense) e(monotone)h(map)g FF(e)p FC(,)g(the)g(r)l(elation)g FF(e)2366 3901 y FJ(\005)2437 3889 y FC(is)g(a)f(split)h(epimorphism)i (with)e(the)f(splitting)208 3989 y(given)d(by)g FF(e)571 3959 y FJ(\005)609 3989 y FC(.)125 4155 y(Mor)l(e)l(over,)35 b(the)d(functor)h FL(\()p FK(\000)o FL(\))1080 4167 y FJ(\005)1151 4155 y FC(is)g(universal)g(w.r.t.)48 b(these)33 b(thr)l(e)l(e)f(pr)l(op)l(erties)i(in)e(the)h(fol)t(lowing)i(sense:)44 b(if)34 b FI(K)e FC(is)h(any)0 4255 y(2-c)l(ate)l(gory)g(wher)l(e)f (the)g(isomorphism)i(2-c)l(el)t(ls)f(ar)l(e)f(identities,)h(to)f(give)h (a)f(2-functor)g FF(H)h FL(:)27 b FI(Rel)o FL(\()p FI(Pre)q FL(\))g FK(\000)-15 b(!)27 b FI(K)32 b FC(is)g(the)g(same)0 4354 y(thing)e(as)g(to)g(give)h(a)f(2-functor)f FF(F)35 b FL(:)24 b FI(Pre)f FK(\000)-14 b(!)23 b FI(K)29 b FC(with)h(the)g (fol)t(lowing)j(thr)l(e)l(e)c(pr)l(op)l(erties:)0 4404 y SDict begin H.S end 0 4404 a 0 4404 a SDict begin 12 H.A end 0 4404 a 0 4404 a SDict begin [/View [/XYZ H.V]/Dest (Item.41) cvn /DEST pdfmark end 0 4404 a Black 98 4520 a FC(1.)p Black 43 w(Every)h FF(F)12 b(f)38 b FC(has)31 b(a)f(right)h(adjoint,)g(denote)l(d)g(by)f FL(\()p FF(F)12 b(f)d FL(\))1907 4490 y Fz(r)1944 4520 y FC(.)0 4574 y SDict begin H.S end 0 4574 a 0 4574 a SDict begin 12 H.A end 0 4574 a 0 4574 a SDict begin [/View [/XYZ H.V]/Dest (Item.42) cvn /DEST pdfmark end 0 4574 a Black 98 4686 a FC(2.)p Black 43 w(F)-6 b(or)30 b(every)g(exact)g(squar)l(e)g(\()1089 4686 y SDict begin H.S end 1089 4686 a Black FC(3.3)p Black 1199 4633 a SDict begin H.R end 1199 4633 a 1199 4686 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 1199 4686 a FC(\))f(the)h(e)l(quality)h FF(F)12 b(f)1819 4656 y Fz(r)1873 4686 y FK(\001)19 b FF(F)12 b(g)26 b FL(=)c FF(F)12 b(p)2240 4698 y FE(0)2296 4686 y FK(\001)18 b FL(\()p FF(F)12 b(p)2476 4698 y FE(1)2513 4686 y FL(\))2545 4656 y Fz(r)2612 4686 y FC(holds.)0 4740 y SDict begin H.S end 0 4740 a 0 4740 a SDict begin 12 H.A end 0 4740 a 0 4740 a SDict begin [/View [/XYZ H.V]/Dest (Item.43) cvn /DEST pdfmark end 0 4740 a Black 98 4852 a FC(3.)p Black 43 w(F)-6 b(or)37 b(every)h(absolutely)g(dense)g(monotone)g(map)f FF(e)p FC(,)j FF(F)12 b(e)36 b FC(is)i(a)g(split)g(epimorphism,)k(with) 37 b(the)h(splitting)g(given)f(by)208 4952 y FL(\()p FF(F)12 b(e)p FL(\))376 4922 y Fz(r)412 4952 y FC(.)p Black 1908 5400 a FL(18)p Black eop end end %%Page: 19 19 TeXDict begin HPSdict begin 19 18 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.19) cvn /DEST pdfmark end -8 -8 a Black Black Black 0 83 a FC(Pr)l(o)l(of.)p Black 43 w FL(It)28 b(is)f(trivial)d(to) j(see)g(that)h(\()p FK(\000)p FL(\))1225 95 y FJ(\005)1291 83 y FL(has)f(the)h(ab)r(o)n(v)n(e)e(three)i(prop)r(erties.)125 183 y(Giv)n(en)j(a)g(2-functor)h FF(H)37 b FL(:)31 b FI(Rel)o FL(\()p FI(Pre)q FL(\))g FK(\000)-14 b(!)31 b FI(K)p FL(,)i(de\014ne)f FF(F)44 b FL(to)32 b(b)r(e)h(the)g(comp)r (osite)c FF(H)g FK(\001)21 b FL(\()p FK(\000)p FL(\))2947 195 y FJ(\005)2986 183 y FL(.)50 b(Suc)n(h)33 b FF(F)44 b FL(clearly)29 b(has)j(the)0 282 y(ab)r(o)n(v)n(e)26 b(three)i(prop)r(erties,)d(since)i(2-functors)f(preserv)n(e)g (adjunctions.)125 382 y(Con)n(v)n(ersely)-7 b(,)21 b(giv)n(en)h FF(F)35 b FL(:)23 b FI(Pre)h FK(\000)-15 b(!)24 b FI(K)p FL(,)g(de\014ne)g FF(H)7 b FB(A)42 b FL(=)22 b FF(F)12 b FB(A)43 b FL(on)23 b(ob)5 b(jects,)25 b(and)e(on)h(a)f(relation)e FF(R)j FL(=)f(\()p FF(d)3293 352 y Fz(R)3293 403 y FE(0)3348 382 y FL(\))3380 394 y FJ(\005)3429 382 y FK(\001)11 b FL(\()p FF(d)3538 352 y Fz(R)3538 403 y FE(1)3593 382 y FL(\))3625 352 y FJ(\005)3688 382 y FL(de\014ne)0 482 y FF(H)c FL(\()p FF(R)q FL(\))23 b(=)g FF(F)12 b(d)423 451 y Fz(R)423 502 y FE(0)496 482 y FK(\001)18 b FL(\()p FF(F)12 b(d)677 451 y Fz(R)677 502 y FE(1)732 482 y FL(\))764 451 y Fz(r)801 482 y FL(,)28 b(where)f(\()p FF(F)12 b(d)1232 451 y Fz(R)1232 502 y FE(1)1287 482 y FL(\))1319 451 y Fz(r)1384 482 y FL(is)26 b(the)i(righ)n(t)e(adjoin)n(t)g(of)i FF(F)12 b(d)2295 451 y Fz(R)2295 502 y FE(1)2377 482 y FL(in)27 b FI(K)p FL(.)125 581 y(It)h(is)g(easy)f(to)h(v)n(erify)f (that)i FF(H)35 b FL(so)27 b(de\014ned)i(preserv)n(es)e(iden)n(tities:) 35 b(the)29 b(iden)n(tit)n(y)e(relation)e FC(id)3074 593 y Ft(A)3172 581 y FL(on)j FB(A)47 b FL(is)27 b(represen)n(ted)0 681 y(as)g(a)g(\014bration)1818 780 y(1)1860 792 y Ft(A)1929 780 y FF(=)p FL(1)2013 792 y Ft(A)1680 883 y Fz(p)1714 891 y Fl(0)1644 1021 y Fy(})p Fx(})p FA(z)1672 997 y(z)1700 973 y(z)1728 949 y(z)1756 925 y(z)1784 901 y(z)1812 877 y(z)1841 853 y(z)2153 883 y Fz(p)2187 891 y Fl(1)2256 1021 y Fy(!)p Fx(!)2225 994 y FA(D)2197 970 y(D)2168 946 y(D)2140 922 y(D)2112 898 y(D)2084 874 y(D)2056 850 y(D)2028 826 y(D)1533 1100 y FB(A)681 b(A)0 1237 y FL(coming)25 b(from)h(the)i(exact)f(comma)e(square)1589 1368 y SDict begin H.S end 1589 1368 a 25 w FL(1)1656 1380 y Ft(A)1725 1368 y FF(=)p FL(1)1809 1380 y Ft(A)1969 1311 y Fz(p)2003 1319 y Fl(1)2102 1347 y Fy(/)p Fx(/)p 1903 1349 200 4 v 1655 1514 a Fz(p)1689 1522 y Fl(0)1746 1605 y Fy(\017)p Fx(\017)p 1744 1605 4 191 v 1925 1521 a FJ(\045)2127 1368 y FB(A)2195 1521 y FE(1)2228 1530 y Fo(A)2170 1605 y Fy(\017)p Fx(\017)p 2168 1605 4 212 v 1703 1688 a FB(A)1913 1729 y FE(1)1946 1738 y Fo(A)2102 1667 y Fy(/)p Fx(/)p 1814 1668 289 4 v 2127 1688 a FB(A)2311 1368 y SDict begin 12 H.A end 2311 1368 a 2311 1368 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.9) cvn /DEST pdfmark end 2311 1368 a Black 1418 w FL(\(4.9\))p Black 0 1879 a(Hence)j FF(H)7 b FL(\()p FC(id)431 1891 y Ft(A)501 1879 y FL(\))23 b(=)g FF(F)12 b(p)751 1891 y FE(0)806 1879 y FK(\001)19 b FL(\()p FF(F)12 b(p)987 1891 y FE(1)1024 1879 y FL(\))1056 1849 y Fz(r)1116 1879 y FL(=)23 b FF(F)12 b FL(\(1)1343 1891 y Ft(A)1412 1879 y FL(\))24 b(=)e(1)1597 1891 y Fz(F)9 b Ft(A)1741 1879 y FL(=)22 b(1)1870 1891 y Fz(H)t Ft(A)2026 1879 y FL(holds)k(b)n(y)i(our)e(assumptions)f(on)j FF(F)12 b FL(.)125 1979 y(F)-7 b(or)27 b(preserv)-5 b(ation)25 b(of)i(comp)r(osition)d(use)k(Corollary)1812 1979 y SDict begin H.S end 1812 1979 a Black FL(3.7)p Black 1918 1925 a SDict begin H.R end 1918 1925 a 1918 1979 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.7) cvn H.B /ANN pdfmark end 1918 1979 a FL(:)37 b(\014rst)1155 2155 y FF(H)7 b FL(\()p FF(S)e FL(\))18 b FK(\001)h FF(H)7 b FL(\()p FF(R)q FL(\))23 b(=)f FF(F)12 b(d)1833 2120 y Fz(S)1833 2175 y FE(0)1900 2155 y FK(\001)18 b FL(\()p FF(F)12 b(d)2081 2120 y Fz(S)2081 2175 y FE(1)2130 2155 y FL(\))2162 2120 y Fz(r)2217 2155 y FK(\001)19 b FF(F)12 b(d)2367 2120 y Fz(R)2367 2175 y FE(0)2440 2155 y FK(\001)19 b FL(\()p FF(F)12 b(d)2622 2120 y Fz(R)2622 2175 y FE(1)2676 2155 y FL(\))2708 2120 y Fz(r)0 2330 y FL(b)n(y)27 b(de\014nition.)36 b(F)-7 b(urther,)27 b(b)n(y)g(exactness)g(of)h(the)g(pullbac)n(k)d (from)h(Corollary)2457 2330 y SDict begin H.S end 2457 2330 a Black FL(3.7)p Black 2563 2277 a SDict begin H.R end 2563 2277 a 2563 2330 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.7) cvn H.B /ANN pdfmark end 2563 2330 a 28 w FL(and)h(our)g(assumption)e(on)i FF(F)12 b FL(,)28 b(w)n(e)f(ha)n(v)n(e)895 2506 y FF(F)12 b(d)1003 2472 y Fz(S)1003 2527 y FE(0)1069 2506 y FK(\001)19 b FL(\()p FF(F)12 b(d)1251 2472 y Fz(S)1251 2527 y FE(1)1299 2506 y FL(\))1331 2472 y Fz(r)1387 2506 y FK(\001)18 b FF(F)12 b(d)1536 2472 y Fz(R)1536 2527 y FE(0)1609 2506 y FK(\001)19 b FL(\()p FF(F)12 b(d)1791 2472 y Fz(R)1791 2527 y FE(1)1846 2506 y FL(\))1878 2472 y Fz(r)1938 2506 y FL(=)23 b FF(F)12 b(d)2134 2472 y Fz(S)2134 2527 y FE(0)2200 2506 y FK(\001)19 b FF(F)12 b(q)2344 2518 y FE(0)2399 2506 y FK(\001)19 b FL(\()p FF(F)12 b(q)2575 2518 y FE(1)2612 2506 y FL(\))2644 2472 y Fz(r)2700 2506 y FK(\001)18 b FL(\()p FF(F)12 b(d)2881 2472 y Fz(R)2881 2527 y FE(1)2936 2506 y FL(\))2968 2472 y Fz(r)0 2682 y FL(and,)27 b(\014nally)-7 b(,)26 b(since)g FF(F)12 b(w)31 b FL(is)26 b(split)g(epi)h(b)n(y)g(Corollary) 1694 2682 y SDict begin H.S end 1694 2682 a Black FL(3.7)p Black 1800 2628 a SDict begin H.R end 1800 2628 a 1800 2682 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.7) cvn H.B /ANN pdfmark end 1800 2682 a 28 w FL(and)h(our)e(assumption)f (on)j FF(F)12 b FL(,)27 b(w)n(e)h(obtain)645 2858 y FF(F)12 b(d)753 2823 y Fz(S)753 2878 y FE(0)820 2858 y FK(\001)19 b FF(F)12 b(q)964 2870 y FE(0)1019 2858 y FK(\001)19 b FF(F)12 b(w)21 b FK(\001)d FL(\()p FF(F)12 b(w)r FL(\))1437 2823 y Fz(r)1494 2858 y FK(\001)18 b FL(\()p FF(F)12 b(q)1669 2870 y FE(1)1707 2858 y FL(\))1739 2823 y Fz(r)1794 2858 y FK(\001)19 b FL(\()p FF(F)12 b(d)1976 2823 y Fz(R)1976 2878 y FE(1)2031 2858 y FL(\))2063 2823 y Fz(r)2123 2858 y FL(=)22 b FF(F)12 b(d)2318 2823 y Fz(R)p FJ(\001)p Fz(S)2318 2878 y FE(0)2455 2858 y FK(\001)19 b FL(\()p FF(F)12 b(d)2637 2823 y Fz(R)p FJ(\001)p Fz(S)2637 2878 y FE(1)2755 2858 y FL(\))2787 2823 y Fz(r)2847 2858 y FL(=)23 b FF(H)7 b FL(\()p FF(R)19 b FK(\001)g FF(S)5 b FL(\))0 3033 y(and)27 b(the)h(pro)r(of)f(is)g(complete.)p 3839 3033 4 57 v 3843 2981 50 4 v 3843 3033 V 3893 3033 4 57 v 0 3198 a FM(Remark.)74 b FL(There)21 b(is)g(an)h(analogous)d (theorem)h(with)i(\\)p FI(P)n(os)n FL(")g(replacing)d(\\)p FI(Pre)p FL(")i(and)h(\\surjectiv)n(e")e(replacing)e(\\absolutely)0 3298 y(dense".)0 3422 y SDict begin H.S end 0 3422 a 0 3422 a SDict begin 12 H.A end 0 3422 a 0 3422 a SDict begin [/View [/XYZ H.V]/Dest (section.5) cvn /DEST pdfmark end 0 3422 a 149 x FN(5)135 b(The)44 b(extension)h(theorem)0 3753 y SDict begin H.S end 0 3753 a 0 3753 a SDict begin 12 H.A end 0 3753 a 0 3753 a SDict begin [/View [/XYZ H.V]/Dest (theorem.5.1) cvn /DEST pdfmark end 0 3753 a Black FM(De\014nition)g(5.1.)p Black 48 w FL(W)-7 b(e)40 b(sa)n(y)f(that)h(a) g(lo)r(cally)c(monotone)i(functor)i FF(T)55 b FL(:)43 b FI(Pre)h FK(\000)-14 b(!)44 b FI(Pre)c FL(satis\014es)e(the)j FC(Be)l(ck-Cheval)t(ley)0 3852 y(Condition)36 b FL(\(BCC\))28 b(if)f(it)g(preserv)n(es)e(exact)i(squares.)0 4013 y SDict begin H.S end 0 4013 a 0 4013 a SDict begin 12 H.A end 0 4013 a 0 4013 a SDict begin [/View [/XYZ H.V]/Dest (theorem.5.2) cvn /DEST pdfmark end 0 4013 a Black FM(Remark)k(5.2.)p Black 41 w FL(A)d(functor)g(satisfying)e(the)i(BCC)g(has)g(to)g (preserv)n(e)e(order-em)n(b)r(eddings,)f(absolutely)g(dense)j(monotone) 0 4113 y(maps)20 b(and)i(absolute)e(left)h(Kan)g(extensions.)33 b(This)21 b(follo)n(ws)e(from)h(Example)2412 4113 y SDict begin H.S end 2412 4113 a Black FL(3.3)p Black 2518 4059 a SDict begin H.R end 2518 4059 a 2518 4113 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.3) cvn H.B /ANN pdfmark end 2518 4113 a FL(.)35 b(Examples)19 b(of)i(functors)h(\(not\))g (satisfying)0 4212 y(the)28 b(BCC)f(can)h(b)r(e)g(found)g(in)e(Section) 1235 4212 y SDict begin H.S end 1235 4212 a Black FL(6)p Black 1276 4159 a SDict begin H.R end 1276 4159 a 1276 4212 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.6) cvn H.B /ANN pdfmark end 1276 4212 a FL(.)0 4373 y SDict begin H.S end 0 4373 a 0 4373 a SDict begin 12 H.A end 0 4373 a 0 4373 a SDict begin [/View [/XYZ H.V]/Dest (theorem.5.3) cvn /DEST pdfmark end 0 4373 a Black FM(Theorem)k(5.3.)p Black 40 w FC(F)-6 b(or)30 b(a)h(2-functor)e FF(T)34 b FL(:)24 b FI(Pre)f FK(\000)-14 b(!)23 b FI(Pre)30 b FC(the)g(fol)t(lowing)i(ar)l(e)e(e)l(quivalent:)0 4418 y SDict begin H.S end 0 4418 a 0 4418 a SDict begin 12 H.A end 0 4418 a 0 4418 a SDict begin [/View [/XYZ H.V]/Dest (Item.44) cvn /DEST pdfmark end 0 4418 a Black 98 4533 a FC(1.)p Black 43 w(Ther)l(e)g(is)g(a)g(2-functor)p 969 4467 61 4 v 30 w FF(T)k FL(:)23 b FI(Rel)p FL(\()p FI(Pre)p FL(\))h FK(\000)-15 b(!)24 b FI(Rel)o FL(\()p FI(Pre)q FL(\))30 b FC(such)f(that)1470 4915 y SDict begin H.S end 1470 4915 a 1511 4763 a FI(Rel)p FL(\()p FI(Pre)p FL(\))p 2030 4669 49 3 v 2030 4717 a Fz(T)2278 4742 y Fy(/)p Fx(/)p 1830 4744 449 4 v 2303 4763 a FI(Rel)o FL(\()p FI(Pre)q FL(\))1599 5082 y FI(Pre)2030 5126 y Fz(T)2365 5061 y Fy(/)p Fx(/)p 1742 5063 624 4 v 1495 4916 a FE(\()p FJ(\000)p FE(\))1599 4924 y Fq(\005)1658 4808 y Fy(O)p Fx(O)p 1656 5000 4 192 v 2390 5082 a FI(Pre)2474 4916 y FE(\()p FJ(\000)p FE(\))2578 4924 y Fq(\005)2449 4808 y Fy(O)p Fx(O)p 2448 5000 V 2638 4915 a SDict begin 12 H.A end 2638 4915 a 2638 4915 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.10) cvn /DEST pdfmark end 2638 4915 a Black 1050 w FL(\(5.10\))p Black Black 1908 5400 a(19)p Black eop end end %%Page: 20 20 TeXDict begin HPSdict begin 20 19 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.20) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.45) cvn /DEST pdfmark end 0 0 a Black 98 83 a FC(2.)p Black 43 w(The)30 b(functor)g FF(T)41 b FC(satis\014es)30 b(the)f(BCC.)0 132 y SDict begin H.S end 0 132 a 0 132 a SDict begin 12 H.A end 0 132 a 0 132 a SDict begin [/View [/XYZ H.V]/Dest (Item.46) cvn /DEST pdfmark end 0 132 a Black 98 249 a FC(3.)p Black 43 w(Ther)l(e)f(is)g(a)g (distributive)g(law)56 b FF(T)24 b FK(\001)14 b Fv(L)23 b FK(\000)-14 b(!)23 b Fv(L)14 b FK(\001)g FF(T)50 b FC(of)29 b FF(T)38 b FC(over)28 b(the)g(KZ)f(do)l(ctrine)h FL(\()p Fv(L)p FF(;)14 b Fv(y)p FF(;)g Fv(m)p FL(\))28 b FC(describ)l(e)l(d)h(in)f(\()3508 249 y SDict begin H.S end 3508 249 a Black FC(2.2)p Black 3618 196 a SDict begin H.R end 3618 196 a 3618 249 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.2) cvn H.B /ANN pdfmark end 3618 249 a FC(\))f(ab)l(ove.)p Black 0 415 a(Pr)l(o)l(of.)p Black 43 w FL(The)g(equiv)-5 b(alence)24 b(of)i(1.)g(and)g(3.)g(follo)n (ws)e(from)h(general)f(facts)i(ab)r(out)g(distributiv)n(e)d(la)n(ws,)i (using)g(Prop)r(osition)3794 415 y SDict begin H.S end 3794 415 a Black FL(2.7)p Black 3900 362 a SDict begin H.R end 3900 362 a 3900 415 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.2.7) cvn H.B /ANN pdfmark end 3900 415 a 0 515 a FL(ab)r(o)n(v)n(e.)36 b(See,)27 b(e.g.,)g([)636 527 y SDict begin H.S end 636 527 a Black -12 x FL(S)682 527 y FE(1)p Black 720 458 a SDict begin H.R end 720 458 a 720 515 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.street:monads) cvn H.B /ANN pdfmark end 720 515 a FL(].)37 b(F)-7 b(or)27 b(the)h(equiv)-5 b(alence)25 b(of)j(1.)f(and)g(2.,)h(observ)n(e)d(that) j FF(T)39 b FL(satis\014es)26 b(the)i(BCC)f(i\013)1511 756 y FI(Pre)1692 710 y Fz(T)1778 735 y Fy(/)p Fx(/)p 1654 736 125 4 v 1803 756 a FI(Pre)1940 695 y FE(\()p FJ(\000)o FE(\))2043 703 y Fq(\005)2071 735 y Fy(/)p Fx(/)p 1947 736 V 2096 756 a FI(Rel)o FL(\()p FI(Pre)q FL(\))0 950 y(satis\014es)f(the)i(three)f(prop)r(erties)f(of)h(Theorem) 1497 950 y SDict begin H.S end 1497 950 a Black FL(4.1)p Black 1603 897 a SDict begin H.R end 1603 897 a 1603 950 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.4.1) cvn H.B /ANN pdfmark end 1603 950 a 28 w FL(ab)r(o)n(v)n(e.)p 2820 950 4 57 v 2824 897 50 4 v 2824 950 V 2873 950 4 57 v 3839 950 V 3843 897 50 4 v 3843 950 V 3893 950 4 57 v 0 1116 a FM(Remark.)78 b FL(There)27 b(is)f(an)i(analogous)c (theorem)i(with)h(\\)p FI(P)n(os)o FL(")g(replacing)d(\\)p FI(Pre)p FL(".)0 1282 y SDict begin H.S end 0 1282 a 0 1282 a SDict begin 12 H.A end 0 1282 a 0 1282 a SDict begin [/View [/XYZ H.V]/Dest (theorem.5.4) cvn /DEST pdfmark end 0 1282 a Black FM(Corollary)33 b(5.4.)p Black 40 w FC(If)d FF(T)41 b FC(is)30 b(a)g(lo)l(c)l(al)t(ly)i(monotone)e (functor,)g(the)g(lifting)p 2283 1216 61 4 v 30 w FF(T)41 b FC(is)30 b(c)l(ompute)l(d)g(as)p 1527 1398 V 1527 1465 a FF(T)11 b FL(\()p FF(R)q FL(\))24 b(=)e(\()p FF(T)12 b(d)1962 1477 y FE(0)1999 1465 y FL(\))2031 1477 y FJ(\005)2088 1465 y FK(\001)18 b FL(\()p FF(T)12 b(d)2265 1477 y FE(1)2302 1465 y FL(\))2334 1431 y FJ(\005)0 1648 y FC(wher)l(e)30 b FL(\()p FF(d)309 1660 y FE(0)347 1648 y FF(;)14 b FB(E)h FF(;)f(d)526 1660 y FE(1)563 1648 y FL(\))30 b FC(is)h(the)f(two-side)l (d)g(discr)l(ete)h(\014br)l(ation)f(c)l(orr)l(esp)l(onding)h(to)e FF(R)q FC(.)0 1863 y FM(Corollary)-8 b(.)143 b FL(Let)38 b FF(T)50 b FL(:)40 b FI(Pre)g FK(\000)-15 b(!)40 b FI(Pre)e FL(and)f FF(T)1583 1875 y FE(0)1660 1863 y FL(:)i FI(Set)h FK(\000)-14 b(!)39 b FI(Set)f FL(suc)n(h)f(that)h FF(T)12 b(D)41 b FL(=)e FF(D)r(T)2981 1875 y FE(0)3055 1863 y FL(and)f FF(V)19 b(T)50 b FL(=)39 b FF(T)3546 1875 y FE(0)3583 1863 y FF(V)57 b FL(where)0 1963 y FF(V)46 b FL(:)27 b FI(Pre)g FK(\000)-14 b(!)26 b FI(Set)k FL(is)f(the)h (forgetful)f(functor)h(and)f FF(D)j FL(is)d(its)g(left-adjoin)n(t.)42 b(Then)30 b FF(T)41 b FL(satis\014es)28 b(the)i(BCC)g(i\013)f FF(T)3504 1975 y FE(0)3571 1963 y FL(preserv)n(es)0 2063 y(w)n(eak)e(pullbac)n(ks.)p Black 0 2229 a FC(Pr)l(o)l(of.)p Black 43 w FL(W)-7 b(e)23 b(sho)n(w)e(that)p 773 2162 V 23 w FF(T)33 b FL(preserv)n(es)21 b(comp)r(osition)d(of)23 b(relations)c(if)p 2157 2162 86 4 v 21 w FF(T)2206 2241 y FE(0)2266 2229 y FL(do)r(es.)34 b(By)22 b(Corollary)2970 2229 y SDict begin H.S end 2970 2229 a Black FL(5.4)p Black 3076 2175 a SDict begin H.R end 3076 2175 a 3076 2229 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.4) cvn H.B /ANN pdfmark end 3076 2229 a 23 w FL(and)g(the)h(corollary)17 b(after)0 2328 y(Prop)r(osition)448 2328 y SDict begin H.S end 448 2328 a Black FL(2.13)p Black 596 2275 a SDict begin H.R end 596 2275 a 596 2328 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.2.13) cvn H.B /ANN pdfmark end 596 2328 a FL(,)29 b(w)n(e)f(ha)n(v)n(e)g FI(Rel)o FL(\()p FF(V)19 b FL(\))p 1205 2262 61 4 v FF(T)37 b FL(=)p 1380 2262 86 4 v 24 w FF(T)1429 2340 y FE(0)1466 2328 y FI(Rel)o FL(\()p FF(V)20 b FL(\).)40 b(Let)29 b FF(S;)14 b(R)30 b FL(b)r(e)f(t)n(w)n(o)f(monotone)f(relations.)37 b(W)-7 b(e)29 b(ha)n(v)n(e)f FI(Rel)o FL(\()p FF(V)19 b FL(\))p 3709 2262 61 4 v FF(T)12 b FL(\()p FF(S)24 b FK(\001)0 2428 y FF(R)q FL(\))g(=)p 209 2361 86 4 v 24 w FF(T)258 2440 y FE(0)295 2428 y FI(Rel)o FL(\()p FF(V)19 b FL(\)\()p FF(S)24 b FK(\001)19 b FF(R)q FL(\))24 b(=)p 894 2361 V 24 w FF(T)943 2440 y FE(0)980 2428 y FL(\()p FI(Rel)o FL(\()p FF(V)c FL(\))p FF(S)j FK(\001)c FI(Rel)p FL(\()p FF(V)g FL(\))p FF(R)q FL(\))24 b(=)p 1821 2361 V 24 w FF(T)1870 2440 y FE(0)1907 2428 y FL(\()p FI(Rel)o FL(\()p FF(V)c FL(\))p FF(S)5 b FL(\))19 b FK(\001)p 2330 2361 V 19 w FF(T)2379 2440 y FE(0)2415 2428 y FL(\()p FI(Rel)p FL(\()p FF(V)g FL(\))p FF(R)q FL(\))25 b(=)e FI(Rel)p FL(\()p FF(V)c FL(\))p 3140 2361 61 4 v FF(T)11 b FL(\()p FF(S)5 b FL(\))19 b FK(\001)g FI(Rel)p FL(\()p FF(V)g FL(\))p 3623 2361 V FF(T)11 b FL(\()p FF(R)q FL(\))24 b(=)0 2528 y FI(Rel)o FL(\()p FF(V)c FL(\)\()p 274 2461 V FF(T)11 b(S)23 b FK(\001)p 450 2461 V 19 w FF(T)11 b(R)q FL(\),)28 b(hence)p 887 2461 V 27 w FF(T)11 b FL(\()p FF(S)24 b FK(\001)18 b FF(R)q FL(\))23 b(=)p 1302 2461 V 23 w FF(T)11 b(S)23 b FK(\001)p 1478 2461 V 19 w FF(T)11 b(R)28 b FL(b)n(y)f FI(Rel)p FL(\()p FF(V)19 b FL(\))28 b(b)r(eing)e(faithful.)125 2627 y(Con)n(v)n(ersely)-7 b(,)31 b(an)n(y)i(pullbac)n(k)e(in)i FI(Set)g FL(is)f(mapp)r(ed)h(b)n (y)g FF(D)j FL(to)d(a)g(pullbac)n(k)e(in)i FI(Pre)h FL(and)f(then)h(to) f(an)g(exact)g(square)f(b)n(y)0 2727 y FF(T)12 b FL(.)49 b(No)n(w)32 b(from)f FF(T)12 b(D)31 b FL(=)f FF(D)r(T)904 2739 y FE(0)973 2727 y FL(and)i(the)g(fact)h(that)f(an)n(y)f(exact)h (square)e(of)i(sets)g(is)f(a)h(w)n(eak)f(pullbac)n(k)e(it)j(follo)n(ws) d(that)j FF(T)3863 2739 y FE(0)0 2826 y FL(preserv)n(es)26 b(w)n(eak)g(pullbac)n(ks.)p 3839 2826 4 57 v 3843 2774 50 4 v 3843 2826 V 3893 2826 4 57 v 0 2968 a SDict begin H.S end 0 2968 a 0 2968 a SDict begin 12 H.A end 0 2968 a 0 2968 a SDict begin [/View [/XYZ H.V]/Dest (section.6) cvn /DEST pdfmark end 0 2968 a 133 x FN(6)135 b(Examples)0 3283 y SDict begin H.S end 0 3283 a 0 3283 a SDict begin 12 H.A end 0 3283 a 0 3283 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.1) cvn /DEST pdfmark end 0 3283 a Black FM(Example)27 b(6.1.)p Black 38 w FL(All)c(the)j(\\Kripk)n(e-p)r (olynomi)o(al)o(")18 b(functors)25 b(satisfy)f(the)h(Bec)n(k-Chev)-5 b(alley)21 b(Condition.)34 b(This)24 b(means)g(the)0 3382 y(functors)j(de\014ned)h(b)n(y)g(the)g(follo)n(wing)23 b(grammar:)1162 3565 y FF(T)34 b FL(::=)23 b FC(c)l(onst)1571 3577 y Ft(X)1675 3565 y FK(j)g FC(Id)32 b FK(j)24 b FF(T)1935 3531 y Fz(@)2000 3565 y FK(j)f FF(T)30 b FL(+)18 b FF(T)34 b FK(j)23 b FF(T)29 b FK(\002)18 b FF(T)34 b FK(j)24 b Fv(L)p FF(T)0 3748 y FL(where)j FC(c)l(onst)433 3760 y Ft(X)541 3748 y FL(is)g(the)h(constan)n(t-at-)p FB(X)20 b FL(,)28 b FF(T)1416 3718 y Fz(@)1486 3748 y FL(is)e(the)i FC(dual)37 b FL(of)28 b FF(T)12 b FL(,)27 b(de\014ned)g(b)n(y)h (putting)1617 3930 y FF(T)1678 3896 y Fz(@)1721 3930 y FB(A)41 b FL(=)23 b(\()p FF(T)12 b FB(A)2095 3896 y Fw(op)2173 3930 y FL(\))2205 3896 y Fw(op)0 4113 y FL(and)35 b Fv(L)p FB(X)57 b FL(=)35 b([)p FB(X)579 4083 y Fw(op)656 4113 y FF(;)14 b Fv(2)p FL(])35 b(\(the)h(lo)n(w)n(ersets)c(on)j FB(X)22 b FL(,)37 b(ordered)d(b)n(y)h(inclusion\).)57 b(Observ)n(e)33 b(that)i Fv(L)3051 4083 y Fz(@)3094 4113 y FB(X)58 b FL(=)35 b([)p FB(X)22 b FF(;)14 b Fv(2)p FL(])3559 4083 y Fw(op)3637 4113 y FL(,)37 b(hence)0 4213 y Fv(L)51 4183 y Fz(@)94 4213 y FB(X)45 b FL(=)23 b Fv(U)p FB(X)49 b FL(\(the)29 b(upp)r(ersets)e(on)g FB(X)22 b FL(,)28 b(ordered)e(b)n(y)i(rev)n(ersed)d(inclusion\).)125 4312 y(T)-7 b(o)27 b(c)n(hec)n(k)f(that)i(BCC)g(is)e(satis\014ed,)g (supp)r(ose)i(that)g(the)g(square)1683 4688 y SDict begin H.S end 1683 4688 a 1754 4527 a FB(P)1936 4470 y Fz(p)1970 4478 y Fl(1)2069 4506 y Fy(/)p Fx(/)p 1869 4508 200 4 v 1708 4666 a Fz(p)1742 4674 y Fl(0)1799 4751 y Fy(\017)p Fx(\017)p 1798 4751 4 200 v 1933 4674 a FJ(\045)2094 4527 y FB(B)2158 4666 y Fz(g)2133 4751 y Fy(\017)p Fx(\017)p 2131 4751 V 1756 4834 a FB(A)1951 4878 y Fz(f)2073 4813 y Fy(/)p Fx(/)p 1867 4815 207 4 v 2098 4834 a FB(C)2217 4688 y SDict begin 12 H.A end 2217 4688 a 2217 4688 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.11) cvn /DEST pdfmark end 2217 4688 a Black 1471 w FL(\(6.11\))p Black 0 5061 a(is)e(exact.)p Black 1908 5400 a(20)p Black eop end end %%Page: 21 21 TeXDict begin HPSdict begin 21 20 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.21) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (Item.47) cvn /DEST pdfmark end 0 0 a Black 101 83 a FL(1.)p Black 42 w(The)27 b(functor)h FC(c)l(onst)859 95 y Ft(X)940 83 y FL(.)208 216 y(The)f(image)e(of)j(square)e(\()1006 216 y SDict begin H.S end 1006 216 a Black FL(6.11)p Black 1154 162 a SDict begin H.R end 1154 162 a 1154 216 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.11) cvn H.B /ANN pdfmark end 1154 216 a FL(\))i(under)f FC(c)l(onst)1642 228 y Ft(X)1751 216 y FL(is)f(the)i(square)1829 445 y FB(X)2004 390 y FE(1)2037 399 y Fo(X)2153 424 y Fy(/)p Fx(/)p 1954 426 200 4 v 1754 592 a FE(1)1787 601 y Fo(X)1879 669 y Fy(\017)p Fx(\017)p 1878 669 4 200 v 2021 592 a FJ(\045)2178 445 y FB(X)2253 592 y FE(1)2286 601 y Fo(X)2228 669 y Fy(\017)p Fx(\017)p 2227 669 V 1829 752 a FB(X)2004 794 y FE(1)2037 803 y Fo(X)2153 731 y Fy(/)p Fx(/)p 1954 733 200 4 v 2178 752 a FB(X)208 981 y FL(where)f(the)h(comparison)23 b(is)k(the)h(iden)n(tit)n(y)-7 b(.)35 b(This)27 b(is)f(an)h(exact)g (square)g(\(it)g(is)g(a)g(Y)-7 b(oneda)27 b(square\).)0 1035 y SDict begin H.S end 0 1035 a 0 1035 a SDict begin 12 H.A end 0 1035 a 0 1035 a SDict begin [/View [/XYZ H.V]/Dest (Item.48) cvn /DEST pdfmark end 0 1035 a Black 101 1147 a FL(2.)p Black 42 w(The)g(functor)h FC(Id)9 b FL(.)208 1280 y(This)26 b(functor)i(ob)n(viously)c(satis\014es)i(the) i(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)0 1330 y SDict begin H.S end 0 1330 a 0 1330 a SDict begin 12 H.A end 0 1330 a 0 1330 a SDict begin [/View [/XYZ H.V]/Dest (Item.49) cvn /DEST pdfmark end 0 1330 a Black 101 1446 a FL(3.)p Black 42 w(Supp)r(ose)j FF(T)39 b FL(satis\014es)26 b(the)i(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)208 1579 y(The)j(square)1760 1738 y FB(P)1851 1708 y Fw(op)2007 1674 y Fz(p)2041 1646 y Fm(op)2041 1692 y Fl(0)2152 1717 y Fy(/)p Fx(/)p 1953 1719 200 4 v 1728 1885 a Fz(p)1762 1857 y Fm(op)1762 1903 y Fl(1)1844 1962 y Fy(\017)p Fx(\017)p 1842 1962 4 200 v 2018 1885 a FJ(\045)2177 1738 y FB(A)2263 1708 y Fw(op)2284 1887 y Fz(f)2323 1862 y Fm(op)2259 1962 y Fy(\017)p Fx(\017)p 2257 1962 V 1766 2045 a FB(B)1844 2015 y Fw(op)2008 2092 y Fz(g)2042 2067 y Fm(op)2161 2025 y Fy(/)p Fx(/)p 1947 2026 214 4 v 2185 2045 a FB(C)2255 2015 y Fw(op)208 2244 y FL(is)f(exact)h(b)n(y)g(Example)970 2244 y SDict begin H.S end 970 2244 a Black FL(3.5)p Black 1076 2191 a SDict begin H.R end 1076 2191 a 1076 2244 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.5) cvn H.B /ANN pdfmark end 1076 2244 a 28 w FL(and,)g(b)n(y)h(assumption,)d(so) i(is)f(the)i(square)1639 2486 y FF(T)12 b FL(\()p FB(P)1823 2456 y Fw(op)1900 2486 y FL(\))1973 2423 y Fz(T)d FE(\()p Fz(p)2081 2395 y Fm(op)2081 2441 y Fl(0)2138 2423 y FE(\))2181 2466 y Fy(/)p Fx(/)p 1957 2467 224 4 v 1570 2646 a Fz(T)g FE(\()p Fz(p)1678 2618 y Fm(op)1678 2664 y Fl(1)1735 2646 y FE(\))1786 2731 y Fy(\017)p Fx(\017)p 1784 2731 4 200 v 2018 2646 a FJ(\045)2205 2486 y FF(T)j FB(A)2351 2456 y Fw(op)2342 2646 y Fz(T)d FE(\()p Fz(f)2455 2621 y Fm(op)2512 2646 y FE(\))2317 2731 y Fy(\017)p Fx(\017)p 2316 2731 4 221 v 1645 2818 a FF(T)j FL(\()p FB(B)1816 2788 y Fw(op)1894 2818 y FL(\))1958 2866 y Fz(T)d FE(\()p Fz(g)2066 2841 y Fm(op)2123 2866 y FE(\))2156 2798 y Fy(/)p Fx(/)p 1951 2799 206 4 v 2181 2818 a FF(T)j FL(\()p FB(C)2343 2788 y Fw(op)2421 2818 y FL(\))208 3055 y(Finally)-7 b(,)24 b(the)k(square)1497 3214 y(\()p FF(T)12 b FL(\()p FB(P)1713 3183 y Fw(op)1790 3214 y FL(\)\))1854 3183 y Fw(op)1907 3150 y FE(\()p Fz(T)d FE(\()p Fz(p)2041 3122 y Fm(op)2041 3168 y Fl(1)2098 3150 y FE(\)\))2150 3125 y Fm(op)2156 3193 y Fy(/)p Fx(/)p 1957 3194 200 4 v 1390 3373 a FE(\()p Fz(T)g FE(\()p Fz(p)1524 3345 y Fm(op)1524 3391 y Fl(0)1581 3373 y FE(\)\))1633 3348 y Fm(op)1714 3458 y Fy(\017)p Fx(\017)p 1713 3458 4 200 v 2021 3373 a FJ(\045)2181 3214 y FL(\()p FF(T)j FL(\()p FB(B)2384 3183 y Fw(op)2462 3214 y FL(\)\))2526 3183 y Fw(op)2418 3373 y FE(\()p Fz(T)d FE(\()p Fz(g)2552 3348 y Fm(op)2609 3373 y FE(\)\))2661 3348 y Fm(op)2393 3458 y Fy(\017)p Fx(\017)p 2391 3458 V 1499 3546 a FL(\()p FF(T)j FL(\()p FB(A)1710 3516 y Fw(op)1787 3546 y FL(\)\))1851 3516 y Fw(op)1906 3593 y FE(\()p Fz(T)d FE(\()p Fz(f)2045 3568 y Fm(op)2101 3593 y FE(\)\))2153 3568 y Fm(op)2161 3525 y Fy(/)p Fx(/)p 1954 3527 207 4 v 2186 3546 a FL(\()p FF(T)j FL(\()p FB(C)2380 3516 y Fw(op)2458 3546 y FL(\)\))2522 3516 y Fw(op)208 3749 y FL(is)26 b(exact)h(b)n(y)g(Example)970 3749 y SDict begin H.S end 970 3749 a Black FL(3.5)p Black 1076 3695 a SDict begin H.R end 1076 3695 a 1076 3749 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.5) cvn H.B /ANN pdfmark end 1076 3749 a 28 w FL(and)g(this)g(is)g(what)g(w)n(e)h (w)n(ere)e(supp)r(osed)i(to)f(pro)n(v)n(e.)0 3798 y SDict begin H.S end 0 3798 a 0 3798 a SDict begin 12 H.A end 0 3798 a 0 3798 a SDict begin [/View [/XYZ H.V]/Dest (Item.50) cvn /DEST pdfmark end 0 3798 a Black 101 3915 a FL(4.)p Black 42 w(Supp)r(ose)g(b)r(oth)h FF(T)778 3927 y FE(1)843 3915 y FL(and)f FF(T)1053 3927 y FE(2)1118 3915 y FL(satisfy)f(the)i(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)34 b(W)-7 b(e)28 b(pro)n(v)n(e)e(that)i FF(T)3115 3927 y FE(1)3170 3915 y FL(+)18 b FF(T)3302 3927 y FE(2)3367 3915 y FL(do)r(es)27 b(satisfy)f(it.)208 4047 y(The)h(image)e(of)j(\()745 4047 y SDict begin H.S end 745 4047 a Black FL(6.11)p Black 892 3994 a SDict begin H.R end 892 3994 a 892 4047 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.11) cvn H.B /ANN pdfmark end 892 4047 a FL(\))g(under)g FF(T)1237 4059 y FE(1)1292 4047 y FL(+)18 b FF(T)1424 4059 y FE(2)1489 4047 y FL(is)1413 4281 y FF(T)1462 4293 y FE(1)1499 4281 y FB(P)25 b FL(+)18 b FF(T)1740 4293 y FE(2)1777 4281 y FB(P)1928 4224 y Fz(T)1967 4232 y Fl(1)2000 4224 y Fz(p)2034 4232 y Fl(1)2066 4224 y FE(+)p Fz(T)2156 4232 y Fl(2)2189 4224 y Fz(p)2223 4232 y Fl(1)2291 4260 y Fy(/)p Fx(/)p 1893 4262 399 4 v 1288 4434 a Fz(T)1327 4442 y Fl(1)1360 4434 y Fz(p)1394 4442 y Fl(0)1426 4434 y FE(+)p Fz(T)1516 4442 y Fl(2)1549 4434 y Fz(p)1583 4442 y Fl(0)1641 4518 y Fy(\017)p Fx(\017)p 1639 4518 4 200 v 2053 4435 a FJ(\045)2316 4281 y FF(T)2365 4293 y FE(1)2402 4281 y FB(B)k FL(+)c FF(T)2631 4293 y FE(2)2668 4281 y FB(B)2556 4434 y Fz(T)2595 4442 y Fl(1)2628 4434 y Fz(g)r FE(+)p Fz(T)2752 4442 y Fl(2)2785 4434 y Fz(g)2531 4518 y Fy(\017)p Fx(\017)p 2530 4518 V 1418 4601 a FF(T)1467 4613 y FE(1)1504 4601 y FB(A)37 b FL(+)18 b FF(T)1740 4613 y FE(2)1777 4601 y FB(A)1958 4645 y Fz(T)1997 4653 y Fl(1)2030 4645 y Fz(f)7 b FE(+)p Fz(T)2159 4653 y Fl(2)2191 4645 y Fz(f)2301 4580 y Fy(/)p Fx(/)p 1888 4582 414 4 v 2326 4601 a FF(T)2375 4613 y FE(1)2411 4601 y FB(C)33 b FL(+)18 b FF(T)2631 4613 y FE(2)2668 4601 y FB(C)208 4830 y FL(The)27 b(assertion)e(follo)n(ws)g (from)h(the)i(fact)g(that)g(copro)r(ducts)e(are)h(disjoin)n(t)f(in)h FI(Pre)p FL(.)0 4880 y SDict begin H.S end 0 4880 a 0 4880 a SDict begin 12 H.A end 0 4880 a 0 4880 a SDict begin [/View [/XYZ H.V]/Dest (Item.51) cvn /DEST pdfmark end 0 4880 a Black 101 4997 a FL(5.)p Black 42 w(Supp)r(ose)g(b)r(oth)h FF(T)778 5009 y FE(1)843 4997 y FL(and)f FF(T)1053 5009 y FE(2)1118 4997 y FL(satisfy)f(the)i(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)34 b(W)-7 b(e)28 b(pro)n(v)n(e)e(that)i FF(T)3115 5009 y FE(1)3170 4997 y FK(\002)18 b FF(T)3302 5009 y FE(2)3367 4997 y FL(do)r(es)27 b(satisfy)f(it.)p Black 1908 5400 a(21)p Black eop end end %%Page: 22 22 TeXDict begin HPSdict begin 22 21 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.22) cvn /DEST pdfmark end -8 -8 a Black Black 208 83 a FL(The)27 b(image)e(of)j(\()745 83 y SDict begin H.S end 745 83 a Black FL(6.11)p Black 892 30 a SDict begin H.R end 892 30 a 892 83 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.11) cvn H.B /ANN pdfmark end 892 83 a FL(\))g(under)g FF(T)1237 95 y FE(1)1292 83 y FK(\002)18 b FF(T)1424 95 y FE(2)1489 83 y FL(is)1413 316 y FF(T)1462 328 y FE(1)1499 316 y FB(P)25 b FK(\002)18 b FF(T)1740 328 y FE(2)1777 316 y FB(P)1928 259 y Fz(T)1967 267 y Fl(1)1999 259 y Fz(p)2033 267 y Fl(1)2066 259 y FJ(\002)p Fz(T)2157 267 y Fl(2)2190 259 y Fz(p)2224 267 y Fl(1)2291 295 y Fy(/)p Fx(/)p 1893 297 399 4 v 1287 469 a Fz(T)1326 477 y Fl(1)1359 469 y Fz(p)1393 477 y Fl(0)1425 469 y FJ(\002)p Fz(T)1516 477 y Fl(2)1549 469 y Fz(p)1583 477 y Fl(0)1641 553 y Fy(\017)p Fx(\017)p 1639 553 4 200 v 2053 470 a FJ(\045)2316 316 y FF(T)2365 328 y FE(1)2402 316 y FB(B)k FK(\002)c FF(T)2631 328 y FE(2)2668 316 y FB(B)2556 469 y Fz(T)2595 477 y Fl(1)2628 469 y Fz(g)r FJ(\002)p Fz(T)2753 477 y Fl(2)2786 469 y Fz(g)2531 553 y Fy(\017)p Fx(\017)p 2530 553 V 1418 636 a FF(T)1467 648 y FE(1)1504 636 y FB(A)37 b FK(\002)18 b FF(T)1740 648 y FE(2)1777 636 y FB(A)1958 680 y Fz(T)1997 688 y Fl(1)2029 680 y Fz(f)7 b FJ(\002)p Fz(T)2159 688 y Fl(2)2192 680 y Fz(f)2301 615 y Fy(/)p Fx(/)p 1888 617 414 4 v 2326 636 a FF(T)2375 648 y FE(1)2411 636 y FB(C)33 b FK(\002)18 b FF(T)2631 648 y FE(2)2668 636 y FB(C)208 865 y FL(The)27 b(assertion)e(follo)n(ws)g(from)h(ho)n(w)h(pro)r(ducts) g(are)g(formed)f(in)h FI(Pre)p FL(.)0 914 y SDict begin H.S end 0 914 a 0 914 a SDict begin 12 H.A end 0 914 a 0 914 a SDict begin [/View [/XYZ H.V]/Dest (Item.52) cvn /DEST pdfmark end 0 914 a Black 101 1031 a FL(6.)p Black 42 w(Supp)r(ose)g(that)h FF(T)39 b FL(satis\014es)26 b(the)i(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)34 b(W)-7 b(e)28 b(pro)n(v)n(e)e(that)i Fv(L)p FF(T)39 b FL(do)r(es)27 b(satisfy)f(it)h(again.)208 1163 y(It)g(su\016ces)g(to)g(pro)n(v)n(e)f (that)i Fv(L)f FL(satis\014es)e(the)j(Bec)n(k-Chev)-5 b(alley)24 b(Condition.)34 b(The)28 b(image)c(of)k(square)e(\()3407 1163 y SDict begin H.S end 3407 1163 a Black FL(6.11)p Black 3554 1110 a SDict begin H.R end 3554 1110 a 3554 1163 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.11) cvn H.B /ANN pdfmark end 3554 1163 a FL(\))i(under)f Fv(L)208 1263 y FL(is)f(the)i(square)1807 1409 y Fv(L)p FB(P)2020 1352 y Fn(L)p Fz(p)2093 1360 y Fl(1)2172 1388 y Fy(/)p Fx(/)p 1973 1390 200 4 v 1747 1556 a Fn(L)p Fz(p)1820 1564 y Fl(0)1878 1633 y Fy(\017)p Fx(\017)p 1876 1633 4 200 v 2037 1556 a FJ(\045)2197 1409 y Fv(L)p FB(B)2287 1556 y Fn(L)p Fz(g)2262 1633 y Fy(\017)p Fx(\017)p 2260 1633 V 1809 1716 a Fv(L)p FB(A)2035 1761 y Fn(L)p Fz(f)2177 1695 y Fy(/)p Fx(/)p 1971 1697 207 4 v 2202 1716 a Fv(L)p FB(C)208 1913 y FL(First)23 b(recall)f(ho)n(w)i Fv(L)g FL(is)g(de\014ned)h(on)g(monotone)e(maps:)34 b(for)24 b(example,)f Fv(L)p FF(f)31 b FL(:)23 b Fv(L)p FB(A)42 b FK(\000)-15 b(!)24 b Fv(L)p FB(C)38 b FL(is)24 b(de\014ned)h(as)f(a)g (left)h(Kan)208 2012 y(extension)h(along)f FF(f)846 1982 y Fw(op)946 2012 y FL(:)f FB(A)1078 1982 y Fw(op)1179 2012 y FK(\000)-14 b(!)23 b FB(C)1405 1982 y Fw(op)1483 2012 y FL(.)37 b(This)26 b(means)h(that,)g(for)h(ev)n(ery)e(lo)n(w)n (erset)f FF(W)35 b FL(:)23 b FB(A)3100 1982 y Fw(op)3200 2012 y FK(\000)-14 b(!)23 b Fv(2)p FL(,)1431 2206 y(\()p Fv(L)p FF(f)9 b FL(\)\()p FF(W)j FL(\))23 b(=)1861 2127 y Fu(_)1889 2302 y Fz(a)1967 2206 y FB(C)2036 2172 y Fw(op)2114 2206 y FL(\()p FF(f)2196 2172 y Fw(op)2273 2206 y FF(a;)14 b FK(\000)p FL(\))k FK(^)h FF(W)12 b(a)208 2458 y FL(or,)26 b(in)h(a)g(more)f(readable)f(fashion,)1461 2652 y(\()p Fv(L)p FF(f)9 b FL(\)\()p FF(W)j FL(\))23 b(:)g FF(c)g FK(7!)2014 2573 y Fu(_)2043 2748 y Fz(a)2121 2652 y FB(C)14 b FL(\()p FF(c;)g(f)9 b(a)p FL(\))18 b FK(^)h FF(W)12 b(a)208 2909 y FL(Hence)33 b FF(c)h FL(is)e(in)h(the)h (lo)n(w)n(erset)c(\()p Fv(L)p FF(f)9 b FL(\)\()p FF(W)j FL(\))34 b(i\013)f(there)h(is)e FF(a)h FL(in)g FF(W)46 b FL(suc)n(h)33 b(that)g FF(c)g FK(\024)g FF(f)9 b(a)p FL(.)54 b(Observ)n(e)31 b(that)j Fv(L)f FL(is)g(indeed)208 3009 y(a)f(functor:)48 b(it)33 b(clearly)d(preserv)n(es)h(iden)n (tities)f(and)j(comp)r(osition)d(\(for)j(that,)i(see)d(Theorem)g(4.47)g (of)h([)3511 3009 y SDict begin H.S end 3511 3009 a Black FL(Ke)p Black 3612 2952 a SDict begin H.R end 3612 2952 a 3612 3009 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kelly:book) cvn H.B /ANN pdfmark end 3612 3009 a FL(]\))h(up)f(to)208 3108 y(isomorphisms.)e(But)d(these)g(canonical)c(isomorphisms)e(are)27 b(iden)n(tities,)e(since)h([)p FB(X)2864 3078 y Fw(op)2942 3108 y FF(;)14 b Fv(2)p FL(])28 b(is)e(alw)n(a)n(ys)f(a)i FC(p)l(oset)8 b FL(.)208 3241 y(W)-7 b(e)24 b(emplo)n(y)d(Example)970 3241 y SDict begin H.S end 970 3241 a Black FL(3.4)p Black 1077 3187 a SDict begin H.R end 1077 3187 a 1077 3241 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.3.4) cvn H.B /ANN pdfmark end 1077 3241 a FL(:)35 b(b)r(oth)24 b Fv(L)p FF(f)33 b FL(and)23 b Fv(L)p FF(p)1702 3253 y FE(1)1763 3241 y FL(are)g(left)h(adjoin)n(ts)e(with)i(\()p Fv(L)p FF(f)9 b FL(\))2701 3211 y Fz(r)2761 3241 y FL(=)22 b([)p FF(f)2921 3211 y Fw(op)2999 3241 y FF(;)14 b Fv(2)p FL(])24 b(and)g(\()p Fv(L)p FF(p)3412 3253 y FE(1)3449 3241 y FL(\))3481 3211 y Fz(r)3541 3241 y FL(=)e([)p FF(p)3693 3201 y Fw(op)3693 3263 y FE(1)3771 3241 y FF(;)14 b Fv(2)p FL(].)208 3341 y(Hence)27 b(it)g(su\016ces)h(to)f(pro)n(v)n(e) f(that)1574 3440 y Fv(L)p FF(p)1667 3452 y FE(0)1723 3440 y FK(\001)18 b FL([)p FF(p)1829 3400 y Fw(op)1829 3462 y FE(1)1907 3440 y FF(;)c Fv(2)p FL(])23 b(=)f([)p FF(f)2196 3406 y Fw(op)2274 3440 y FF(;)14 b Fv(2)p FL(])k FK(\001)h Fv(L)p FF(g)208 3589 y FL(Moreo)n(v)n(er,)28 b(b)n(y)j(the)g(densit)n(y)e(of)i(principal)c(lo)n(w)n(ersets)h(of)i (the)h(form)f FB(B)s FL(\()p FK(\000)p FF(;)14 b(b)2646 3601 y FE(0)2683 3589 y FL(\))31 b(in)f Fv(L)p FB(B)k FL(and)d(the)g(fact)f(that)h(all)e(the)208 3689 y(monotone)c(maps)h Fv(L)p FF(p)900 3701 y FE(0)937 3689 y FL(,)i([)p FF(p)1053 3649 y Fw(op)1053 3711 y FE(1)1130 3689 y FF(;)14 b Fv(2)p FL(],)28 b([)p FF(f)1360 3659 y Fw(op)1438 3689 y FF(;)14 b Fv(2)p FL(],)27 b Fv(L)p FF(g)j FL(preserv)n(e)c(suprema)g(\(since)g (they)i(all)d(are)i(left)g(adjoin)n(ts\),)f(it)h(su\016ces)208 3789 y(to)g(pro)n(v)n(e)f(that)1128 3888 y SDict begin H.S end 1128 3888 a FL(\()p Fv(L)p FF(p)1253 3900 y FE(0)1308 3888 y FK(\001)19 b FL([)p FF(p)1415 3848 y Fw(op)1415 3910 y FE(1)1492 3888 y FF(;)14 b Fv(2)p FL(]\)\()p FB(B)s FL(\()p FK(\000)q FF(;)g(b)1911 3900 y FE(0)1948 3888 y FL(\)\))24 b(=)e(\([)p FF(f)2228 3854 y Fw(op)2306 3888 y FF(;)14 b Fv(2)p FL(])19 b FK(\001)f Fv(L)p FF(g)s FL(\)\()p FB(B)s FL(\()p FK(\000)q FF(;)c(b)2879 3900 y FE(0)2915 3888 y FL(\)\))2979 3888 y SDict begin 12 H.A end 2979 3888 a 2979 3888 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.12) cvn /DEST pdfmark end 2979 3888 a Black 709 w FL(\(6.12\))p Black 208 4037 a(holds)26 b(for)h(all)e FF(b)703 4049 y FE(0)740 4037 y FL(.)208 4170 y(The)i(left-hand)g(side)g(is)f (isomorphic)d(to)1135 4364 y Fv(L)p FF(p)1228 4376 y FE(0)1264 4364 y FL(\()p FB(B)s FL(\()p FF(p)1448 4376 y FE(1)1487 4364 y FK(\000)o FF(;)14 b(b)1624 4376 y FE(0)1661 4364 y FL(\)\))24 b(=)e FF(a)h FK(7!)2009 4285 y Fu(_)2031 4459 y Fz(w)2115 4364 y FB(A)c FL(\()p FF(a;)14 b(p)2356 4376 y FE(0)2393 4364 y FF(w)r FL(\))19 b FK(^)g FB(B)s FL(\()p FF(p)2731 4376 y FE(1)2769 4364 y FF(w)r(;)14 b(b)2903 4376 y FE(0)2941 4364 y FL(\))208 4621 y(By)27 b(exactness)f(of)i(\()832 4621 y SDict begin H.S end 832 4621 a Black FL(6.11)p Black 980 4567 a SDict begin H.R end 980 4567 a 980 4621 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.11) cvn H.B /ANN pdfmark end 980 4621 a FL(\),)g(this)f (means)f(that)1427 4803 y Fv(L)p FF(p)1520 4815 y FE(0)1556 4803 y FL(\()p FB(B)s FL(\()p FF(p)1740 4815 y FE(1)1779 4803 y FK(\000)o FF(;)14 b(b)1916 4815 y FE(0)1953 4803 y FL(\)\))24 b(=)e FF(a)h FK(7!)g FB(C)15 b FL(\()p FF(f)9 b(a;)14 b(g)s(b)2613 4815 y FE(0)2649 4803 y FL(\))208 4985 y(Observ)n(e)25 b(further)j(that)1260 5084 y(\()p Fv(L)p FF(g)s FL(\)\()p FB(B)s FL(\()p FK(\000)q FF(;)14 b(b)1699 5096 y FE(0)1735 5084 y FL(\)\))24 b(=)f FF(c)g FK(7!)2076 5005 y Fu(_)2107 5184 y Fz(b)2182 5084 y FB(C)14 b FL(\()p FF(c;)g(g)s(b)p FL(\))k FK(^)h FB(B)s FL(\()p FF(b;)14 b(b)2778 5096 y FE(0)2815 5084 y FL(\))p Black 1908 5400 a(22)p Black eop end end %%Page: 23 23 TeXDict begin HPSdict begin 23 22 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.23) cvn /DEST pdfmark end -8 -8 a Black Black 208 83 a FL(hence)1485 183 y(\()p Fv(L)p FF(g)s FL(\)\()p FB(B)s FL(\()p FK(\000)q FF(;)14 b(b)1924 195 y FE(0)1960 183 y FL(\)\))24 b(=)f FF(c)g FK(7!)g FB(C)14 b FL(\()p FF(c;)g(g)s(b)2554 195 y FE(0)2591 183 y FL(\))208 319 y(b)n(y)27 b(the)h(Y)-7 b(oneda)27 b(Lemma.)208 447 y(The)g(righ)n(t)f (hand)i(side)e(of)i(\()1080 447 y SDict begin H.S end 1080 447 a Black FL(6.12)p Black 1228 393 a SDict begin H.R end 1228 393 a 1228 447 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.12) cvn H.B /ANN pdfmark end 1228 447 a FL(\))g(is)e (therefore)h(isomorphic)c(to)834 607 y(\([)p FF(f)939 573 y Fw(op)1017 607 y FF(;)14 b Fv(2)p FL(])k FK(\001)h Fv(L)p FF(g)s FL(\)\()p FB(B)s FL(\()p FK(\000)p FF(;)14 b(b)1589 619 y FE(0)1626 607 y FL(\)\))24 b(=)f([)p FF(f)1875 573 y Fw(op)1952 607 y FF(;)14 b Fv(2)p FL(]\()p FF(c)23 b FK(7!)g FB(C)15 b FL(\()p FF(c;)f(g)s(b)2509 619 y FE(0)2545 607 y FL(\)\))24 b(=)e FF(a)h FK(7!)h FB(C)14 b FL(\()p FF(f)9 b(a;)14 b(g)s(b)3205 619 y FE(0)3241 607 y FL(\))0 796 y SDict begin H.S end 0 796 a 0 796 a SDict begin 12 H.A end 0 796 a 0 796 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.2) cvn /DEST pdfmark end 0 796 a Black FM(Example)36 b(6.2.)p Black 44 w FL(Recall)30 b(the)k(adjunction)e FF(Q)f FK(a)h FF(I)39 b FL(:)32 b FI(P)n(os)f FK(\000)-14 b(!)32 b FI(Pre)q FL(,)i(where)f FF(I)40 b FL(is)31 b(the)j(inclusion)c(functor)i(and)h FF(Q)p FL(\()p FB(A)19 b FL(\))33 b(is)0 896 y(the)g(quotien)n(t)e(of)h FB(A)52 b FL(obtained)31 b(b)n(y)h(iden)n(tifying)e FF(a)i FL(and)g FF(b)g FL(whenev)n(er)g FF(a)f FK(\024)f FF(b)j FL(and)f FF(b)f FK(\024)f FF(a)p FL(.)52 b(The)32 b(functors)g FF(Q)g FL(and)h FF(I)39 b FL(are)0 995 y(lo)r(cally)27 b(monotone)i(and)i(map)e(exact)i(squares)e(to)i(exact)f(squares.)45 b(Hence,)32 b(if)e FF(T)39 b FL(:)29 b FI(Pre)g FK(\000)-15 b(!)29 b FI(Pre)i FL(satis\014es)e(the)i(BCC,)g(so)0 1095 y(do)r(es)c FF(QT)12 b(I)29 b FL(:)23 b FI(P)n(os)f FK(\000)-14 b(!)23 b FI(P)n(os)o FL(.)0 1243 y SDict begin H.S end 0 1243 a 0 1243 a SDict begin 12 H.A end 0 1243 a 0 1243 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.3) cvn /DEST pdfmark end 0 1243 a Black FM(Example)35 b(6.3.)p Black 42 w FL(The)d FC(p)l(owerset)i(functor)41 b Fv(P)30 b FL(:)g FI(Pre)g FK(\000)-14 b(!)30 b FI(Pre)i FL(is)e(de\014ned)i(as)f(follo)n(ws.)47 b(The)31 b(order)g(on)g Fv(P)p FB(A)51 b FL(is)30 b(the)i(Egli-)0 1343 y(Milner)25 b(preorder,)h(that)i(is,)f Fv(P)p FL(\()p FF(A;)14 b(B)t FL(\))24 b(=)e(1)28 b(if)f(and)g(only)f(if)1106 1503 y SDict begin H.S end 1106 1503 a FK(8)p FF(a)c FK(2)h FF(A)28 b FK(9)p FF(b)23 b FK(2)g FF(B)32 b(a)23 b FK(\024)g FF(b)k FL(and)h FK(8)p FF(b)21 b FK(2)j FF(B)32 b FK(9)p FF(a)23 b FK(2)g FF(A)28 b(a)23 b FK(\024)g FF(b)2795 1503 y SDict begin 12 H.A end 2795 1503 a 2795 1503 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.13) cvn /DEST pdfmark end 2795 1503 a Black 893 w FL(\(6.13\))p Black 0 1663 a Fv(P)p FF(f)9 b FL(\()p FF(A)p FL(\))28 b(is)f(the)h(direct)e (image)f(of)i FF(A)p FL(.)38 b(The)27 b(functor)h Fv(P)g FL(is)e(lo)r(cally)e(monotone)i(and)h(satis\014es)f(the)i(BCC.)125 1763 y(The)h FC(\014nitary)i(p)l(owerset)g(functor)e Fv(P)1273 1775 y Fz(!)1350 1763 y FL(is)f(de\014ned)h(similarly:)34 b Fv(P)2150 1775 y Fz(!)2198 1763 y FB(A)48 b FL(consists)27 b(of)i(the)g(\014nite)f(subsets)h(of)g FB(A)48 b FL(equipp)r(ed)0 1862 y(with)27 b(the)h(Egli-Milner)22 b(preorder.)35 b Fv(P)1187 1874 y Fz(!)1263 1862 y FL(is)27 b(lo)r(cally)d(monotone)h (and)j(satis\014es)e(the)i(BCC.)125 1962 y(The)k(p)r(o)n(w)n(erset)f (functor)h Fv(P)h FL(is)e(lo)r(cally)e(monotone)h(and)i(satis\014es)f (the)i(BCC.)f(This)f(follo)n(ws)e(from)i(the)i(unn)n(um)n(b)r(ered)0 2062 y(corollary)23 b(of)28 b(Section)729 2062 y SDict begin H.S end 729 2062 a Black FL(5)p Black 771 2008 a SDict begin H.R end 771 2008 a 771 2062 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.5) cvn H.B /ANN pdfmark end 771 2062 a FL(.)37 b(F)-7 b(or)27 b(a)g(direct)f(argumen)n(t)g (consider)f(an)j(exact)f(square:)1683 2415 y SDict begin H.S end 1683 2415 a 1754 2254 a FB(P)1936 2197 y Fz(p)1970 2205 y Fl(1)2069 2233 y Fy(/)p Fx(/)p 1869 2235 200 4 v 1708 2393 a Fz(p)1742 2401 y Fl(0)1799 2478 y Fy(\017)p Fx(\017)p 1798 2478 4 200 v 1933 2401 a FJ(\045)2094 2254 y FB(B)2158 2393 y Fz(g)2133 2478 y Fy(\017)p Fx(\017)p 2131 2478 V 1756 2561 a FB(A)1951 2605 y Fz(f)2073 2540 y Fy(/)p Fx(/)p 1867 2542 207 4 v 2098 2561 a FB(C)2217 2415 y SDict begin 12 H.A end 2217 2415 a 2217 2415 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.14) cvn /DEST pdfmark end 2217 2415 a Black 1471 w FL(\(6.14\))p Black 0 2773 a(By)g(\()162 2773 y SDict begin H.S end 162 2773 a Black FL(3.5)p Black 269 2719 a SDict begin H.R end 269 2719 a 269 2773 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.5) cvn H.B /ANN pdfmark end 269 2773 a FL(\))h(w)n(e)f(ha)n (v)n(e)f(to)i(sho)n(w)e(that)i(for)f FF(A)d FK(2)f Fv(P)p FB(A)47 b FL(and)27 b FF(B)g FK(2)d Fv(P)p FB(B)867 2949 y SDict begin H.S end 867 2949 a Fv(P)p FB(C)15 b FL(\()p Fv(P)p FF(f)9 b FL(\()p FF(A)p FL(\))p FF(;)14 b Fv(P)p FF(g)s FL(\()p FF(B)t FL(\)\))24 b(=)1659 2871 y Fu(_)1669 3049 y Fz(W)1765 2949 y Fv(P)p FB(A)18 b FL(\()p FF(A;)c Fv(P)p FF(p)2129 2961 y FE(0)2167 2949 y FL(\()p FF(W)e FL(\)\))19 b FK(^)g Fv(P)p FB(B)s FL(\()p Fv(P)p FF(p)2704 2961 y FE(1)2742 2949 y FL(\()p FF(W)12 b FL(\))p FF(;)i(B)t FL(\))3032 2949 y SDict begin 12 H.A end 3032 2949 a 3032 2949 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.15) cvn /DEST pdfmark end 3032 2949 a Black 656 w FL(\(6.15\))p Black 0 3188 a(Assume)27 b Fv(P)p FB(C)14 b FL(\()p Fv(P)p FF(f)9 b FL(\()p FF(A)p FL(\))p FF(;)14 b Fv(P)p FF(g)s FL(\()p FF(B)t FL(\)\))24 b(=)f(1.)36 b(Then)1014 3348 y SDict begin H.S end 1014 3348 a FK(8)p FF(a)22 b FK(2)h FF(A)28 b FK(9)p FF(b)23 b FK(2)g FF(B)32 b(f)9 b(a)23 b FK(\024)f FF(g)s(b)27 b FL(and)h FK(8)p FF(b)21 b FK(2)j FF(B)32 b FK(9)p FF(a)23 b FK(2)g FF(A)28 b(f)9 b(a)23 b FK(\024)f FF(g)s(b)2887 3348 y SDict begin 12 H.A end 2887 3348 a 2887 3348 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.16) cvn /DEST pdfmark end 2887 3348 a Black 801 w FL(\(6.16\))p Black 0 3508 a(W)-7 b(e)37 b(ha)n(v)n(e)f(to)h(\014nd)g FF(W)51 b FK(2)39 b Fv(P)p FB(P)k FL(suc)n(h)37 b(that)g Fv(P)p FB(A)19 b FL(\()p FF(A;)14 b Fv(P)p FF(p)1793 3520 y FE(0)1830 3508 y FL(\()p FF(W)e FL(\)\))38 b(and)f Fv(P)p FB(B)s FL(\()p Fv(P)p FF(p)2483 3520 y FE(1)2521 3508 y FL(\()p FF(W)12 b FL(\))p FF(;)i(B)t FL(\).)66 b(Let)37 b FF(W)50 b FL(=)38 b FK(f)p FF(w)j FK(2)e FB(P)45 b FK(j)39 b(9)p FF(a)g FK(2)0 3608 y FF(A)f(a)h FK(\024)g FF(p)329 3620 y FE(0)366 3608 y FF(w)31 b FL(and)c FK(9)p FF(b)39 b FK(2)h FF(B)i(p)980 3620 y FE(1)1017 3608 y FF(w)g FK(\024)d FF(b)p FK(g)p FL(.)66 b(It)38 b(is)e(easy)h(to)g(see)g (that)h FF(W)49 b FL(satis\014es)36 b FK(8)p FF(w)41 b FK(2)f FF(W)50 b FK(9)p FF(a)39 b FK(2)h FF(A)e FB(A)19 b FL(\()p FF(a;)14 b(p)3598 3620 y FE(0)3635 3608 y FF(w)r FL(\))38 b(and)0 3708 y FK(8)p FF(w)32 b FK(2)f FF(W)44 b FK(9)p FF(b)31 b FK(2)g FF(B)36 b FB(B)s FL(\()p FF(p)796 3720 y FE(1)834 3708 y FF(w)r(;)14 b(b)p FL(\).)51 b(Consider)30 b FF(a)h FK(2)f FF(A)p FL(.)51 b(By)32 b(\()1888 3708 y SDict begin H.S end 1888 3708 a Black FL(6.16)p Black 2036 3654 a SDict begin H.R end 2036 3654 a 2036 3708 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.16) cvn H.B /ANN pdfmark end 2036 3708 a FL(\))g(there)g(exists)f FF(b)f FK(2)h FF(B)36 b FL(suc)n(h)c(that)h FB(C)14 b FL(\()p FF(f)9 b(a;)14 b(g)s(b)p FL(\).)50 b(By)31 b(\()3761 3708 y SDict begin H.S end 3761 3708 a Black FL(3.5)p Black 3868 3654 a SDict begin H.R end 3868 3654 a 3868 3708 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.5) cvn H.B /ANN pdfmark end 3868 3708 a FL(\))0 3807 y(there)26 b(exists)g FF(w)f FK(2)f FF(W)38 b FL(suc)n(h)27 b(that)g FB(A)18 b FL(\()p FF(a;)c(p)1325 3819 y FE(0)1362 3807 y FF(w)r FL(\).)38 b(So)26 b Fv(P)p FB(A)19 b FL(\()p FF(A;)14 b Fv(P)p FF(p)1995 3819 y FE(0)2032 3807 y FL(\()p FF(W)e FL(\)\))24 b(=)f(1.)36 b(Similarly)-7 b(,)21 b(w)n(e)27 b(can)f(sho)n(w)g(that)g(for)g(all)f FF(b)d FK(2)i FF(B)0 3907 y FL(exists)i FF(w)g FK(2)d FF(W)40 b FL(with)27 b FB(B)s FL(\()p FF(p)851 3919 y FE(1)889 3907 y FF(w)r(;)14 b(b)p FL(\).)38 b(This)26 b(sho)n(ws)h(that)g Fv(P)h FL(preserv)n(es)e(exact)h(squares,)f(hence)i(it)f(satis\014es)e(the)j (BCC.)125 4007 y(The)f(pro)r(of)g(that)h Fv(P)745 4019 y Fz(!)821 4007 y FL(satis\014es)e(the)i(BCC)f(go)r(es)g(along)e(the)j (same)e(lines.)0 4155 y SDict begin H.S end 0 4155 a 0 4155 a SDict begin 12 H.A end 0 4155 a 0 4155 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.4) cvn /DEST pdfmark end 0 4155 a Black FM(Example)g(6.4.)p Black 36 w FL(Giv)n(en)c(a)h(preorder)f FB(A)d FL(,)24 b(a)f(subset)h FF(A)f FK(\022)g FB(A)42 b FL(is)22 b(called)f FC(c)l(onvex)34 b FL(if)23 b FF(x)h FK(\024)e FF(y)k FK(\024)d FF(z)j FL(and)e FF(x;)14 b(z)26 b FK(2)e FF(A)g FL(imply)d FF(y)k FK(2)f FF(A)p FL(.)125 4254 y(The)33 b FC(c)l(onvex)i(p)l(owerset)g (functor)42 b Fv(P)1272 4224 y Fz(c)1339 4254 y FL(:)32 b FI(P)n(os)f FK(\000)-14 b(!)33 b FI(P)n(os)f FL(is)g(de\014ned)i(as)e (follo)n(ws.)51 b Fv(P)2737 4224 y Fz(c)2771 4254 y FB(A)h FL(is)32 b(the)h(set)g(of)h(con)n(v)n(ex)d(subsets)0 4354 y(of)h FB(A)50 b FL(endo)n(w)n(ed)31 b(with)g(the)h(Egli-Milner)27 b(order.)48 b Fv(P)1654 4324 y Fz(c)1688 4354 y FF(f)9 b FL(\()p FF(A)p FL(\))32 b(is)e(the)j(direct)d(image)f(of)j FF(A)p FL(.)50 b(This)30 b(is)h(a)g(w)n(ell)f(de\014ned)i(lo)r(cally)0 4454 y(monotone)26 b(functor.)36 b(Notice)27 b(that)g Fv(P)1196 4423 y Fz(c)1253 4431 y FK(\030)1253 4458 y FL(=)1341 4454 y FF(Q)p Fv(P)p FF(I)7 b FL(.)36 b(This)27 b(follo)n(ws)d(from)i(the)i(fact)f(that)h(if)f FB(A)46 b FL(is)26 b(a)h(p)r(oset)g(and)g FF(A;)14 b(B)28 b FK(2)23 b Fv(P)p FF(I)7 b FB(A)19 b FL(,)0 4553 y(then)34 b Fv(P)p FF(I)7 b FB(A)19 b FL(\()p FF(A;)14 b(B)t FL(\))34 b(=)e(1)h(and)h Fv(P)p FF(I)7 b FB(A)18 b FL(\()p FF(B)t(;)c(A)p FL(\))34 b(=)f(1)g(if)g(and)h(only)e(if)h FF(A)h FL(and)f FF(B)38 b FL(ha)n(v)n(e)32 b(the)i(same)e(con)n(v)n(ex)g(h)n(ull.)53 b(Hence,)35 b(b)n(y)0 4653 y(Example)345 4653 y SDict begin H.S end 345 4653 a Black FL(6.2)p Black 451 4599 a SDict begin H.R end 451 4599 a 451 4653 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.6.2) cvn H.B /ANN pdfmark end 451 4653 a FL(,)28 b Fv(P)555 4623 y Fz(c)616 4653 y FL(satis\014es)e(the)i(BCC.)125 4752 y(The)37 b FC(\014nitely-gener)l (ate)l(d)h(c)l(onvex)h(p)l(owerset)45 b Fv(P)1640 4722 y Fz(c)1640 4773 y(!)1726 4752 y FL(is)36 b(de\014ned)h(similarly)31 b(to)37 b Fv(P)2627 4722 y Fz(c)2661 4752 y FL(.)66 b(The)37 b(only)e(di\013erence)h(is)g(that)i(the)0 4852 y(con)n(v)n(ex)22 b(sets)i(app)r(earing)e(in)h Fv(P)955 4822 y Fz(c)955 4873 y(!)1003 4852 y FB(A)42 b FL(are)23 b(con)n(v)n(ex)g(h)n(ulls)e (of)j(\014nitely)f(man)n(y)f(elemen)n(ts)g(of)h FB(A)c FL(.)36 b(Then)24 b Fv(P)3134 4822 y Fz(c)3134 4873 y(!)3206 4852 y FL(is)f(lo)r(cally)d(monotone)0 4952 y(and)27 b(is)e(isomorphic)e(to)k FF(Q)p Fv(P)883 4964 y Fz(!)930 4952 y FF(I)7 b FL(,)27 b(th)n(us)g(it)g(also)d(satis\014es)h(the)i (BCC.)g(Again,)f(w)n(e)g(ha)n(v)n(e)g(that)h Fv(P)2938 4922 y Fz(c)2938 4972 y(!)3009 4952 y FL(=)c FF(Q)p Fv(P)3216 4964 y Fz(!)3263 4952 y FF(I)34 b FL(and)27 b Fv(P)3547 4922 y Fz(c)3547 4972 y(!)3622 4952 y FL(satis\014es)0 5051 y(the)h(BCC.)125 5151 y(Observ)n(e)d(that)j(b)r(oth)g(functors)g (are)e(self-dual:)35 b(\()p Fv(P)1727 5121 y Fz(c)1761 5151 y FL(\))1793 5121 y Fz(@)1859 5151 y FL(=)23 b Fv(P)2000 5121 y Fz(c)2062 5151 y FL(and)k(\()p Fv(P)2308 5121 y Fz(c)2308 5171 y(!)2356 5151 y FL(\))2388 5121 y Fz(@)2455 5151 y FL(=)c Fv(P)2596 5121 y Fz(c)2596 5171 y(!)2644 5151 y FL(.)p Black 1908 5400 a(23)p Black eop end end %%Page: 24 24 TeXDict begin HPSdict begin 24 23 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.24) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a SDict begin H.S end 0 83 a 0 83 a SDict begin 12 H.A end 0 83 a 0 83 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.5) cvn /DEST pdfmark end 0 83 a Black FM(Example)31 b(6.5.)p Black 41 w FL(Since)c(the)i(lo)n(w)n(erset)d(functor)i Fv(L)c FL(:)g FI(Pre)h FK(\000)-14 b(!)24 b FI(Pre)29 b FL(satis\014es)d(the)j(Bec)n(k-Chev)-5 b(alley)25 b(Condition)h(b)n (y)i(Exam-)0 218 y(ple)126 218 y SDict begin H.S end 126 218 a Black FL(6.1)p Black 232 164 a SDict begin H.R end 232 164 a 232 218 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.6.1) cvn H.B /ANN pdfmark end 232 218 a FL(,)21 b(w)n(e)e(can)g(compute)f(its)h(lifting)p 1204 151 51 4 v 17 w Fv(L)j FL(:)i FI(Rel)o FL(\()p FI(Pre)p FL(\))g FK(\000)-14 b(!)23 b FI(Rel)o FL(\()p FI(Pre)q FL(\).)34 b(W)-7 b(e)20 b(sho)n(w)e(ho)n(w)p 2644 151 V 19 w Fv(L)h FL(w)n(orks)f(on)h(the)h(relation)k FB(A)3676 217 y FA(\025)p 3582 199 100 4 v 3657 172 a Fz(R)3782 197 y Fy(/)p Fx(/)p 3682 199 V 3790 218 a FB(B)12 b FL(.)0 317 y(The)31 b(v)-5 b(alue)p 391 251 51 4 v 29 w Fv(L)p FL(\()p FF(R)q FL(\))30 b(is,)h(b)n(y)f(Theorems)1215 317 y SDict begin H.S end 1215 317 a Black FL(4.1)p Black 1321 264 a SDict begin H.R end 1321 264 a 1321 317 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.4.1) cvn H.B /ANN pdfmark end 1321 317 a 31 w FL(and)1516 317 y SDict begin H.S end 1516 317 a Black FL(5.3)p Black 1622 264 a SDict begin H.R end 1622 264 a 1622 317 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.3) cvn H.B /ANN pdfmark end 1622 317 a FL(,)h(giv)n(en)e(b)n (y)h(\()p Fv(L)p FF(d)2140 329 y FE(0)2178 317 y FL(\))2210 329 y FJ(\005)2269 317 y FK(\001)20 b FL(\()p Fv(L)p FF(d)2438 329 y FE(1)2475 317 y FL(\))2507 287 y FJ(\005)2576 317 y FL(where)30 b(\()p FF(d)2894 329 y FE(0)2932 317 y FF(;)14 b FB(E)3031 287 y Fz(R)3086 317 y FF(;)g(d)3166 329 y FE(1)3203 317 y FL(\))28 b(:)g FB(A)46 b FK(\000)-14 b(!)28 b FB(B)34 b FL(is)c(the)0 417 y(t)n(w)n(o-sided)h(discrete)g (\014bration)g(corresp)r(onding)f(to)j FF(R)q FL(.)52 b(Using)32 b(the)h(form)n(ula)d(\()2541 417 y SDict begin H.S end 2541 417 a Black FL(2.1)p Black 2647 363 a SDict begin H.R end 2647 363 a 2647 417 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.1) cvn H.B /ANN pdfmark end 2647 417 a FL(\))j(for)g(relation)c(comp)r(osition,)i(w)n(e)h(can)0 517 y(write)1006 616 y SDict begin H.S end 1006 616 a 1006 550 51 4 v Fv(L)o FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))25 b(=)1526 537 y Fu(_)1537 715 y Fz(W)1632 616 y Fv(L)p FB(B)s FL(\()p FF(B)t(;)14 b Fv(L)p FF(d)1991 628 y FE(0)2029 616 y FL(\()p FF(W)e FL(\)\))20 b FK(^)e Fv(L)p FB(A)h FL(\()p Fv(L)p FF(d)2571 628 y FE(1)2608 616 y FL(\()p FF(W)12 b FL(\))p FF(;)i(A)p FL(\))2893 616 y SDict begin 12 H.A end 2893 616 a 2893 616 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.17) cvn /DEST pdfmark end 2893 616 a Black 795 w FL(\(6.17\))p Black 0 840 a(where)31 b FF(B)h FL(:)d FB(B)469 810 y Fw(op)577 840 y FK(\000)-15 b(!)29 b Fv(2)i FL(and)g FF(A)e FL(:)g FB(A)1210 810 y Fw(op)1316 840 y FK(\000)-14 b(!)29 b Fv(2)i FL(are)f(arbitrary)e(lo)n(w)n(ersets.)45 b(Since)30 b Fv(L)p FF(d)2764 852 y FE(1)2832 840 y FL(is)g(a)h(left)f(adjoin)n(t) g(to)h(restriction)0 940 y(along)25 b FF(d)264 900 y Fw(op)264 962 y FE(1)365 940 y FL(:)e(\()p FB(E)506 909 y Fz(R)560 940 y FL(\))592 909 y Fw(op)693 940 y FK(\000)-14 b(!)23 b FB(A)936 909 y Fw(op)1014 940 y FL(,)k(w)n(e)g(can)h(rewrite)e (\()1653 940 y SDict begin H.S end 1653 940 a Black FL(6.17)p Black 1800 886 a SDict begin H.R end 1800 886 a 1800 940 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.6.17) cvn H.B /ANN pdfmark end 1800 940 a FL(\))i(to)p 1005 1074 51 4 v 1005 1140 a Fv(L)o FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))25 b(=)1525 1061 y Fu(_)1536 1239 y Fz(W)1631 1140 y Fv(L)p FB(B)s FL(\()p FF(B)t(;)14 b Fv(L)p FF(d)1990 1152 y FE(0)2028 1140 y FL(\()p FF(W)e FL(\)\))20 b FK(^)e Fv(L)p FB(E)2420 1106 y Fz(R)2475 1140 y FL(\()p FF(W)n(;)c(A)19 b FK(\001)f FF(d)2785 1100 y Fw(op)2785 1162 y FE(1)2863 1140 y FL(\))0 1397 y(and,)27 b(b)n(y)h(the)g(Y)-7 b(oneda)27 b(Lemma,)e(to)p 1321 1430 V 1321 1496 a Fv(L)p FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))24 b(=)f Fv(L)p FB(B)s FL(\()p FF(B)t(;)14 b Fv(L)p FF(d)2201 1508 y FE(0)2239 1496 y FL(\()p FF(A)19 b FK(\001)f FF(d)2436 1456 y Fw(op)2436 1519 y FE(1)2514 1496 y FL(\)\))0 1646 y(Hence)28 b(the)g(lo)n(w)n (ersets)c FF(B)32 b FL(and)c FF(A)g FL(are)e(related)g(b)n(y)p 1618 1579 V 27 w Fv(L)p FL(\()p FF(R)q FL(\))i(if)f(and)h(only)e(if)h (the)h(inclusion)1642 1828 y FF(B)f FK(\022)22 b Fv(L)p FF(d)1913 1840 y FE(0)1951 1828 y FL(\()p FF(A)d FK(\001)f FF(d)2148 1789 y Fw(op)2148 1851 y FE(1)2226 1828 y FL(\))0 2011 y(holds)26 b(in)h([)p FB(B)415 1981 y Fw(op)494 2011 y FF(;)14 b Fv(2)p FL(].)37 b(Recall)25 b(that)1098 2210 y Fv(L)p FF(d)1192 2222 y FE(0)1229 2210 y FL(\()p FF(A)19 b FK(\001)f FF(d)1426 2170 y Fw(op)1426 2233 y FE(1)1504 2210 y FL(\))24 b(=)e FF(b)h FK(7!)1812 2131 y Fu(_)1833 2306 y Fz(w)1918 2210 y FB(B)s FL(\()p FF(b;)14 b(d)2144 2222 y FE(0)2182 2210 y FF(w)r FL(\))20 b FK(^)e FL(\()p FF(A)h FK(\001)g FF(d)2566 2170 y Fw(op)2566 2233 y FE(1)2644 2210 y FL(\)\()p FF(w)r FL(\))0 2470 y(Therefore)26 b(the)i(inclusion)c FF(B)j FK(\022)22 b Fv(L)p FF(d)1136 2482 y FE(0)1174 2470 y FL(\()p FF(A)c FK(\001)f FF(d)1369 2430 y Fw(op)1369 2493 y FE(1)1447 2470 y FL(\))28 b(is)e(equiv)-5 b(alen)n(t)25 b(to)i(the)h(statemen)n (t:)35 b(F)-7 b(or)27 b(all)e FF(b)i FL(in)f FF(B)32 b FL(there)27 b(is)f(\()p FF(b)3526 2482 y FE(1)3563 2470 y FF(;)14 b(a)3644 2482 y FE(1)3681 2470 y FL(\))27 b(suc)n(h)0 2570 y(that)h FF(R)q FL(\()p FF(b)312 2582 y FE(1)349 2570 y FF(;)14 b(a)430 2582 y FE(1)467 2570 y FL(\))28 b(and)f FF(b)c FK(\024)f FF(b)870 2582 y FE(1)935 2570 y FL(and)27 b FF(a)1140 2582 y FE(1)1205 2570 y FL(in)g FF(A)p FL(.)125 2670 y(Observ)n(e)d(that)i(the)g(ab)r(o)n(v)n (e)f(condition)f(is)g(reminiscen)n(t)f(of)j(one)f(half)g(of)h(the)h (Egli-Milner-st)n(y)o(l)o(e)20 b(of)26 b(the)h(relation)c(lifting)0 2769 y(of)29 b(a)f(p)r(o)n(w)n(erset)g(functor.)40 b(This)28 b(is)f(b)r(ecause)i Fv(L)f FL(is)g(the)h(\\lo)n(w)n(er)d(half)6 b(")28 b(of)h(t)n(w)n(o)f(p)r(ossible)e(\\p)r(o)n(w)n(erpreorder)f (functors".)40 b(The)0 2869 y(\\upp)r(er)27 b(half)6 b(")27 b(is)f(giv)n(en)g(b)n(y)i Fv(U)23 b FL(:)g FI(Pre)g FK(\000)-14 b(!)23 b FI(Pre)28 b FL(where)f Fv(U)c FL(=)g Fv(L)1942 2839 y Fz(@)1985 2869 y FL(.)0 3035 y SDict begin H.S end 0 3035 a 0 3035 a SDict begin 12 H.A end 0 3035 a 0 3035 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.6) cvn /DEST pdfmark end 0 3035 a Black FM(Example)45 b(6.6.)p Black 48 w FL(The)40 b(relation)e(liftings)p 1395 2968 54 4 v 37 w Fv(P)p FL(,)p 1515 2968 87 4 v 44 w Fv(P)1568 3011 y Fz(c)1602 3035 y FL(,)p 1669 2968 102 4 v 44 w Fv(P)1722 3047 y Fz(!)1770 3035 y FL(,)p 1836 2968 V 43 w Fv(P)1889 3011 y Fz(c)1889 3055 y(!)1978 3035 y FL(of)i(the)h(\(con)n(v)n(ex\))f(p)r(o)n(w)n(erset)f(functor)h (and)g(their)g(\014nitary)0 3174 y(v)n(ersions)32 b(yield)g(the)j (\\Egli-Milner")29 b(st)n(yle)k(of)h(the)h(relation)d(lifting.)55 b(More)34 b(precisely)-7 b(,)33 b(for)h(a)g(relation)40 b FB(B)3563 3173 y FA(\025)p 3469 3155 100 4 v 3544 3129 a Fz(R)3669 3154 y Fy(/)p Fx(/)p 3569 3155 V 3677 3174 a FB(A)61 b FL(w)n(e)0 3274 y(ha)n(v)n(e)p 191 3207 54 4 v 26 w Fv(P)p FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))29 b(\(resp)r(ectiv)n(ely)p 1116 3207 102 4 v 25 w Fv(P)1169 3286 y Fz(!)1217 3274 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\),)p 1627 3207 87 4 v 29 w Fv(P)1680 3250 y Fz(c)1714 3274 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)g(A)p FL(\),)p 2124 3207 102 4 v 29 w Fv(P)2177 3250 y Fz(c)2177 3294 y(!)2225 3274 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)g(A)p FL(\)\))29 b(if)e(and)h(only)e(if)1040 3457 y FK(8)p FF(a)c FK(2)h FF(A)28 b FK(9)p FF(b)23 b FK(2)g FF(B)32 b(R)q FL(\()p FF(b;)14 b(a)p FL(\))28 b(and)f FK(8)p FF(b)22 b FK(2)h FF(B)32 b FK(9)p FF(a)23 b FK(2)h FF(A)j(R)q FL(\()p FF(b;)14 b(a)p FL(\))p FF(:)0 3679 y FL(T)-7 b(o)25 b(compute)f(the)h(lifting)e(of)i Fv(P)979 3649 y Fz(c)1012 3679 y FL(,)h(consider)d(a)i(monotone)e (relation)30 b FB(A)2326 3678 y FA(\025)p 2233 3660 100 4 v 2307 3633 a Fz(R)2432 3658 y Fy(/)p Fx(/)p 2333 3660 V 2441 3679 a FB(B)37 b FL(and)24 b(the)i(induced)e(\014bration)g(\()p FF(d)3568 3691 y FE(0)3605 3679 y FF(;)14 b FB(E)h FF(;)f(d)3784 3691 y FE(1)3822 3679 y FL(\))23 b(:)0 3779 y FB(A)42 b FK(\000)-15 b(!)24 b FB(B)s FL(.)37 b(W)-7 b(e)28 b(kno)n(w)f(that)p 944 3712 87 4 v 28 w Fv(P)997 3755 y Fz(c)1031 3779 y FL(\()p FF(R)q FL(\))c(=)g(\()p Fv(P)1355 3748 y Fz(c)1389 3779 y FF(d)1432 3791 y FE(0)1469 3779 y FL(\))1501 3791 y FJ(\005)1558 3779 y FK(\001)c FL(\()p Fv(P)1685 3748 y Fz(c)1719 3779 y FF(d)1762 3791 y FE(1)1799 3779 y FL(\))1831 3748 y FJ(\005)1870 3779 y FL(,)28 b(so)956 3978 y SDict begin H.S end 956 3978 a 956 3911 87 4 v Fv(P)1009 3954 y Fz(c)1043 3978 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))24 b(=)1513 3899 y Fu(_)1533 4077 y Fz(E)1619 3978 y Fv(P)1672 3944 y Fz(c)1706 3978 y FB(B)s FL(\()p FF(B)t(;)14 b Fv(P)1973 3944 y Fz(c)2008 3978 y FF(d)2051 3990 y FE(0)2088 3978 y FL(\()p FF(E)5 b FL(\)\))20 b FK(^)e Fv(P)p FB(A)h FL(\()p Fv(P)2567 3944 y Fz(c)2601 3978 y FF(d)2644 3990 y FE(1)2682 3978 y FL(\()p FF(E)5 b FL(\))p FF(;)14 b(A)p FL(\))2943 3978 y SDict begin 12 H.A end 2943 3978 a 2943 3978 a SDict begin [/View [/XYZ H.V]/Dest (equation.6.18) cvn /DEST pdfmark end 2943 3978 a Black 745 w FL(\(6.18\))p Black 125 4250 a(W)-7 b(e)32 b(pro)n(v)n(e)f(that)p 685 4183 87 4 v 32 w Fv(P)738 4226 y Fz(c)772 4250 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))32 b(=)f(1)h(implies)c FK(8)p FF(a)i FK(2)i FF(A)g FK(9)p FF(b)f FK(2)g FF(B)37 b(R)q FL(\()p FF(b;)14 b(a)p FL(\))32 b(and)g FK(8)p FF(b)e FK(2)h FF(B)36 b FK(9)p FF(a)31 b FK(2)h FF(A)g(R)q FL(\()p FF(b;)14 b(a)p FL(\).)51 b(Consider)0 4350 y(a)34 b(witness)f FF(E)40 b FL(and)34 b FF(a)g FK(2)h FF(A)p FL(.)57 b(Since)34 b Fv(P)1230 4319 y Fz(c)1264 4350 y FB(A)18 b FL(\()p Fv(P)1434 4319 y Fz(c)1468 4350 y FF(d)1511 4362 y FE(1)1549 4350 y FL(\()p FF(E)5 b FL(\))p FF(;)14 b(A)p FL(\))35 b(=)f(1,)i(there)e(exists)f(\()p FF(b)2568 4319 y FJ(0)2591 4350 y FF(;)14 b(a)2672 4319 y FJ(0)2695 4350 y FL(\))35 b FK(2)f FF(E)40 b FL(suc)n(h)34 b(that)h FB(A)18 b FL(\()p FF(a)3494 4319 y FJ(0)3518 4350 y FF(;)c(a)p FL(\).)57 b(Since)0 4449 y Fv(P)53 4419 y Fz(c)87 4449 y FB(B)s FL(\()p FF(B)t(;)14 b Fv(P)354 4419 y Fz(c)389 4449 y FF(d)432 4461 y FE(0)469 4449 y FL(\()p FF(E)5 b FL(\)\))37 b(=)e(1,)h(there)f(exists)f FF(b)h FK(2)h FF(B)j FL(suc)n(h)c(that)g FB(B)s FL(\()p FF(b;)14 b(b)2191 4419 y FJ(0)2214 4449 y FL(\).)60 b(Since)34 b FF(R)i FL(is)e(monotone)f(and)i FF(R)q FL(\()p FF(b)3434 4419 y FJ(0)3457 4449 y FF(;)14 b(a)3538 4419 y FJ(0)3561 4449 y FL(\))36 b(=)f(1)f(w)n(e)0 4549 y(obtain)26 b FF(R)q FL(\()p FF(b;)14 b(a)p FL(\))23 b(=)g(1.)36 b(So)27 b FK(8)p FF(a)c FK(2)g FF(A)28 b FK(9)p FF(b)23 b FK(2)g FF(B)32 b(R)q FL(\()p FF(b;)14 b(a)p FL(\).)37 b(The)27 b(second)g(part)g(is)g(analogous.)125 4648 y(Con)n(v)n(ersely)-7 b(,)24 b(if)j FK(8)p FF(a)22 b FK(2)i FF(A)k FK(9)p FF(b)22 b FK(2)i FF(B)32 b(R)q FL(\()p FF(b;)14 b(a)p FL(\))27 b(and)g FK(8)p FF(b)22 b FK(2)i FF(B)31 b FK(9)p FF(a)24 b FK(2)f FF(A)28 b(R)q FL(\()p FF(b;)14 b(a)p FL(\),)27 b(de\014ne)h(the)g(subset)g(of)f FB(E)43 b FL(as)27 b(follo)n(ws:)1391 4831 y FF(E)h FL(=)23 b FK(f)8 b FF(b)1861 4810 y Fy(/)p Fx(/)1821 4812 y Fk(/o)1761 4810 y(/o)1702 4809 y(/o)1869 4831 y FF(a)32 b FK(j)23 b FF(b)f FK(2)i FF(B)t(;)42 b(a)23 b FK(2)g FF(A)p FK(g)0 5014 y FL(Then)30 b FF(E)35 b FL(is)29 b(con)n(v)n(ex,)h(since)e(b)r (oth)j FF(B)j FL(and)c FF(A)g FL(are)f(con)n(v)n(ex.)43 b(Both)30 b Fv(P)2172 4984 y Fz(c)2206 5014 y FB(B)s FL(\()p FF(B)t(;)14 b Fv(P)2473 4984 y Fz(c)2508 5014 y FF(d)2551 5026 y FE(0)2588 5014 y FL(\()p FF(E)5 b FL(\)\))28 b(=)f(1)j(and)f Fv(P)3158 4984 y Fz(c)3192 5014 y FB(A)19 b FL(\()p Fv(P)3363 4984 y Fz(c)3397 5014 y FF(d)3440 5026 y FE(1)3478 5014 y FL(\()p FF(E)5 b FL(\))p FF(;)14 b(A)p FL(\))28 b(=)e(1)0 5113 y(hold)g(for)i(ob)n (vious)d(reasons.)35 b(Hence)p 1183 5047 V 28 w Fv(P)1236 5089 y Fz(c)1269 5113 y FL(\()p FF(R)q FL(\)\()p FF(B)t(;)14 b(A)p FL(\))25 b(=)d(1)27 b(holds.)p Black 1908 5400 a(24)p Black eop end end %%Page: 25 25 TeXDict begin HPSdict begin 25 24 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.25) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a SDict begin H.S end 0 83 a 0 83 a SDict begin 12 H.A end 0 83 a 0 83 a SDict begin [/View [/XYZ H.V]/Dest (theorem.6.7) cvn /DEST pdfmark end 0 83 a Black FM(Example)29 b(6.7.)p Black 39 w FL(T)-7 b(o)26 b(\014nd)h(a)f(functor)h(that)f(do)r (es)g(not)h(satisfy)e(the)i(BCC,)f(it)g(su\016ces,)h(b)n(y)f(Remark) 3175 83 y SDict begin H.S end 3175 83 a Black FL(5.2)p Black 3282 30 a SDict begin H.R end 3282 30 a 3282 83 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.2) cvn H.B /ANN pdfmark end 3282 83 a FL(,)g(to)h(\014nd)g(a)f(lo)r(cally)0 183 y(monotone)e(functor)h FF(T)34 b FL(:)23 b FI(Pre)h FK(\000)-15 b(!)23 b FI(Pre)j FL(that)g(do)r(es)f(not)g(preserv)n(e)f (order-em)n(b)r(eddings.)32 b(F)-7 b(or)25 b(this,)g(let)g FF(T)37 b FL(b)r(e)25 b(the)h FC(c)l(onne)l(cte)l(d)0 282 y(c)l(omp)l(onents)31 b(functor)9 b FL(,)29 b(i.e.,)f FF(T)40 b FL(tak)n(es)27 b(a)i(preorder)e FB(A)47 b FL(to)29 b(the)g(discretely)d(ordered)h(p)r(oset)i(of)f(connected)h(comp)r(onen) n(ts)e(of)0 382 y FB(A)19 b FL(.)37 b FF(T)h FL(do)r(es)28 b(not)f(preserv)n(e)f(em)n(b)r(edding)g FF(f)31 b FL(:)23 b FB(A)42 b FK(\000)-14 b(!)23 b FB(B)31 b FL(indicated)26 b(b)r(elo)n(w.)p 1509 557 2 2 v 1527 557 V 1546 557 V 1565 557 V 1583 557 V 1602 557 V 1620 557 V 1639 557 V 1657 557 V 1676 557 V 1695 557 V 1713 557 V 1732 557 V 1750 557 V 1769 557 V 1787 557 V 1806 557 V 1509 576 V 1509 594 V 1509 611 V 1509 629 V 1509 646 V 1509 664 V 1509 681 V 1509 699 V 1509 716 V 1509 734 V 1509 751 V 1509 769 V 1509 786 V 1509 804 V 1509 821 V 1509 838 V 1810 576 V 1810 594 V 1810 611 V 1810 629 V 1810 646 V 1810 664 V 1810 681 V 1810 699 V 1810 716 V 1810 734 V 1810 751 V 1810 769 V 1810 786 V 1810 804 V 1810 821 V 1810 838 V 1509 858 V 1527 858 V 1546 858 V 1565 858 V 1583 858 V 1602 858 V 1620 858 V 1639 858 V 1657 858 V 1676 858 V 1695 858 V 1713 858 V 1732 858 V 1750 858 V 1769 858 V 1787 858 V 1806 858 V 2090 474 V 2109 474 V 2127 474 V 2146 474 V 2164 474 V 2183 474 V 2201 474 V 2220 474 V 2239 474 V 2257 474 V 2276 474 V 2294 474 V 2313 474 V 2331 474 V 2350 474 V 2369 474 V 2388 474 V 2090 493 V 2090 510 V 2090 527 V 2090 545 V 2090 562 V 2090 579 V 2090 597 V 2090 614 V 2090 631 V 2090 648 V 2090 666 V 2090 683 V 2090 700 V 2090 718 V 2090 735 V 2090 752 V 2090 770 V 2090 787 V 2090 804 V 2090 821 V 2090 839 V 2391 493 V 2391 510 V 2391 527 V 2391 545 V 2391 562 V 2391 579 V 2391 597 V 2391 614 V 2391 631 V 2391 648 V 2391 666 V 2391 683 V 2391 700 V 2391 718 V 2391 735 V 2391 752 V 2391 770 V 2391 787 V 2391 804 V 2391 821 V 2391 839 V 2090 858 V 2109 858 V 2127 858 V 2146 858 V 2164 858 V 2183 858 V 2201 858 V 2220 858 V 2239 858 V 2257 858 V 2276 858 V 2294 858 V 2313 858 V 2331 858 V 2350 858 V 2369 858 V 2388 858 V 1627 933 a Ft(A)530 b(B)1559 719 y FJ(\017)132 b(\017)1558 759 y Fz(a)1728 767 y(b)2141 719 y FJ(\017)g(\017)2140 759 y Fz(a)2309 767 y(b)2224 594 y FJ(\017)2226 552 y Fz(c)2167 692 y FA(\012)2187 660 y(\012)2208 629 y(\012)2292 657 y(4)2271 626 y(4)2250 594 y(4)0 1056 y SDict begin H.S end 0 1056 a 0 1056 a SDict begin 12 H.A end 0 1056 a 0 1056 a SDict begin [/View [/XYZ H.V]/Dest (section.7) cvn /DEST pdfmark end 0 1056 a 91 x FN(7)j(An)44 b(Application:)58 b(Moss's)45 b(Coalgebraic)f(Logic)h(o)l(v)l(er)h(P)l(osets)0 1329 y FL(W)-7 b(e)40 b(sho)n(w)f(ho)n(w)g(to)g(dev)n(elop)f(the)i (basics)e(of)i(Moss's)f(coalgebraic)c(logic)i(o)n(v)n(er)g(p)r(osets.) 73 b(F)-7 b(or)39 b(reasons)f(of)i(space,)i(this)0 1428 y(dev)n(elopmen)n(t)25 b(will)g(b)r(e)j(terse)f(and)g(assume)f(some)g (familiarit)n(y)c(with,)27 b(e.g.,)g(Sections)g(2.2)g(and)g(3.1)g(of)g ([)3268 1428 y SDict begin H.S end 3268 1428 a Black FL(KuL)p Black 3431 1372 a SDict begin H.R end 3431 1372 a 3431 1428 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kurz-leal:mfps09) cvn H.B /ANN pdfmark end 3431 1428 a FL(].)125 1528 y(Since)k(the)i(logics)c(will)h(ha)n(v)n(e)h(prop)r(ositional)d (connectiv)n(es)i(but)j(no)f(negation)f(\(to)h(capture)g(the)h(seman)n (tic)c(order)i(on)0 1628 y(the)d(logical)c(side\))j(w)n(e)h(will)d(use) j(the)g(category)e FI(DL)i FL(of)g(b)r(ounded)h(distributiv)n(e)24 b(lattices.)36 b(W)-7 b(e)29 b(write)e FF(F)35 b FK(a)24 b FF(U)32 b FL(:)24 b FI(DL)f FK(\000)-14 b(!)24 b FI(P)n(os)0 1727 y FL(for)36 b(the)g(ob)n(vious)e(adjunction;)40 b(and)c FF(P)49 b FL(:)37 b FI(P)n(os)1501 1690 y Fw(op)1617 1727 y FK(\000)-15 b(!)38 b FI(DL)e FL(where)f FF(U)9 b(P)j FB(X)59 b FL(=)37 b([)p FB(X)22 b FF(;)14 b Fv(2)p FL(])37 b(and)f FF(S)42 b FL(:)37 b FI(DL)g FK(\000)-14 b(!)38 b FI(P)n(os)3574 1690 y Fw(op)3688 1727 y FL(where)0 1827 y FF(S)5 b(A)26 b FL(=)g FI(DL)p FL(\()p FF(A;)14 b Fv(2)p FL(\).)44 b(Note)30 b(that)g FF(U)9 b(P)38 b FL(=)26 b([)p FK(\000)p FF(;)14 b Fv(2)p FL(])29 b(and)h(recall)c Fv(L)g FL(=)g([\()p FK(\000)p FL(\))2179 1797 y Fw(op)2257 1827 y FF(;)14 b Fv(2)p FL(].)43 b(F)-7 b(urther,)30 b(let)f FF(T)38 b FL(:)26 b FI(P)n(os)g FK(\000)-15 b(!)27 b FI(P)n(os)i FL(b)r(e)h(a)f(lo)r(cally)0 1926 y(monotone)d(\014nitary) g(functor)h(that)h(satis\014es)e(the)i(BCC.)125 2026 y(W)-7 b(e)28 b(de\014ne)f(coalgebraic)d(logic)g(abstractly)i(b)n(y)h (a)g(functor)h FF(L)22 b FL(:)h FI(DL)g FK(\000)-14 b(!)23 b FI(DL)28 b FL(giv)n(en)e(as)1749 2192 y FF(L)d FL(=)g FF(F)12 b(T)2043 2158 y Fz(@)2085 2192 y FF(U)0 2359 y FL(where)23 b(the)i(functor)f FF(T)722 2328 y Fz(@)787 2359 y FL(:)f FI(P)n(os)f FK(\000)-14 b(!)23 b FI(P)n(os)g FL(is)g(giv)n(en)f(b)n(y)i FF(T)1751 2328 y Fz(@)1793 2359 y FB(X)45 b FL(=)23 b(\()p FF(T)12 b FL(\()p FB(X)2229 2328 y Fw(op)2306 2359 y FL(\)\))2370 2328 y Fw(op)2449 2359 y FL(.)35 b(By)24 b(Example)2975 2359 y SDict begin H.S end 2975 2359 a Black FL(6.1)p Black 3081 2305 a SDict begin H.R end 3081 2305 a 3081 2359 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.6.1) cvn H.B /ANN pdfmark end 3081 2359 a FL(,)h FF(T)3190 2328 y Fz(@)3257 2359 y FL(satis\014es)d(the)i(BCC.)0 2458 y(The)30 b(form)n(ulas)d(of)j(the) h(logic)c(are)i(the)i(elemen)n(ts)d(of)i(the)h(initial)26 b FF(L)p FL(-algebra)h FF(F)12 b(T)2570 2428 y Fz(@)2612 2458 y FF(U)d FL(\()p FK(L)p FL(\))28 b FK(\000)-15 b(!)28 b(L)p FL(.)45 b(The)30 b(form)n(ula)d(giv)n(en)h(b)n(y)0 2558 y(some)e FF(\013)d FK(2)h FF(T)424 2528 y Fz(@)466 2558 y FF(U)9 b FL(\()p FK(L)p FL(\))28 b(is)f(written)g(as)g FK(r)p FF(\013:)h FL(The)g(seman)n(tics)c(is)j(giv)n(en)f(b)n(y)h(a)g (natural)f(transformation)1643 2724 y FF(\016)h FL(:)c FF(LP)34 b FK(\000)-14 b(!)23 b FF(P)12 b(T)2180 2690 y Fw(op)0 2890 y FL(Before)27 b(w)n(e)g(de\014ne)h FF(\016)s FL(,)g(w)n(e)f(need)g(for)h(ev)n(ery)e(preorder)g FB(A)18 b FL(,)28 b(the)g(relation)2267 2890 y SDict begin H.S end 2267 2890 a -30 x FE(1)2301 2890 y SDict begin 12 H.L end 2301 2890 a 2301 2890 a SDict begin [/Subtype /Link/Dest (Hfootnote.1) cvn/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [1 0 0] H.B /ANN pdfmark end 2301 2890 a 1653 3094 a FL([)p FB(A)19 b FF(;)14 b Fv(2)p FL(])1970 3093 y FA(\025)p 1876 3075 100 4 v 1924 3040 a FJ(3)1969 3049 y Fo(A)2075 3073 y Fy(/)p Fx(/)p 1976 3075 V 2084 3094 a FB(A)2169 3064 y Fw(op)0 3260 y FL(giv)n(en)26 b(b)n(y)h(the)h(ev)-5 b(aluation)25 b(map)i FI(ev)1135 3272 y Ft(A)1228 3260 y FL(:)c FB(A)37 b FK(\002)18 b FL([)p FB(A)h FF(;)14 b Fv(2)p FL(])23 b FK(\000)-14 b(!)23 b Fv(2)p FL(.)37 b(Observ)n(e)26 b(that)1698 3427 y SDict begin H.S end 1698 3427 a 23 w FK(3)1776 3439 y Ft(A)1846 3427 y FL(=)d(\()p Fv(y)2005 3439 y Ft(A)2071 3422 y Fm(op)2132 3427 y FL(\))2164 3392 y FJ(\005)2202 3427 y SDict begin 12 H.A end 2202 3427 a 2202 3427 a SDict begin [/View [/XYZ H.V]/Dest (equation.7.19) cvn /DEST pdfmark end 2202 3427 a Black 1486 w FL(\(7.19\))p Black 0 3593 a(since)j(\()p Fv(y)274 3605 y Ft(A)341 3589 y Fm(op)401 3593 y FL(\))433 3563 y FJ(\005)472 3593 y FL(\()p FF(a;)14 b(V)19 b FL(\))k(=)g([)p FB(A)18 b FF(;)c Fv(2)p FL(]\()p Fv(y)1080 3605 y Ft(A)1147 3589 y Fm(op)1207 3593 y FF(a;)g(V)19 b FL(\))k(=)g FF(V)c(a)28 b FL(holds)e(b)n(y)h(the)h(Y)-7 b(oneda)27 b(Lemma.)0 3746 y SDict begin H.S end 0 3746 a 0 3746 a SDict begin 12 H.A end 0 3746 a 0 3746 a SDict begin [/View [/XYZ H.V]/Dest (theorem.7.1) cvn /DEST pdfmark end 0 3746 a Black FM(Lemma)j(7.1.)p Black 40 w FC(F)-6 b(or)30 b(every)g(monotone)g(map)h FF(f)g FL(:)23 b FB(A)42 b FK(\000)-14 b(!)23 b FB(B)33 b FC(we)d(have)1489 3950 y FL([)p FB(A)19 b FF(;)14 b Fv(2)p FL(])1947 3949 y FA(\025)p 1729 3931 225 4 v 1902 3895 a FJ(3)1947 3904 y Fo(A)2177 3929 y Fy(/)p Fx(/)p 1953 3931 V 2202 3950 a FB(A)2288 3920 y Fw(op)1493 4215 y FL([)p FB(B)s FF(;)g Fv(2)p FL(])247 b FA(\025)p 1726 4196 228 4 v 1903 4253 a FJ(3)1948 4262 y Fo(B)2181 4195 y Fy(/)p Fx(/)p 1953 4196 V 1577 4056 a FA(U)p 1595 4128 4 67 v 1379 4077 a FE([)p Fz(f)s(;)p Fn(2)p FE(])1508 4052 y Fq(\005)1597 3995 y Fy(O)p Fx(O)p 1595 4062 V 2206 4215 a FB(B)2284 4185 y Fw(op)2264 4047 y FA(U)p 2282 4132 4 79 v 2339 4069 a FE(\()p Fz(f)2404 4044 y Fm(op)2460 4069 y FE(\))2486 4044 y Fq(\005)2284 3975 y Fy(O)p Fx(O)p 2282 4054 V Black 0 4420 a FC(Diagr)l(ammatic)31 b(Pr)l(o)l(of.)p Black 43 w FL(The)d(square)1511 4551 y FB(A)1597 4521 y Fw(op)1851 4494 y Fn(y)1881 4504 y Fo(A)1935 4491 y Fm(op)2147 4530 y Fy(/)p Fx(/)p 1699 4532 449 4 v 1472 4712 a Fz(f)1511 4687 y Fm(op)1593 4800 y Fy(\017)p Fx(\017)p 1591 4800 4 225 v 2172 4551 a Fv(L)p FL(\()p FB(A)19 b FL(\))2298 4711 y Fn(L)p FE(\()p Fz(f)7 b FE(\))2273 4796 y Fy(\017)p Fx(\017)p 2271 4796 4 200 v 1514 4883 a FB(B)1592 4853 y Fw(op)1852 4912 y Fn(y)1882 4922 y Fo(B)1933 4909 y Fm(op)2151 4862 y Fy(/)p Fx(/)p 1696 4864 456 4 v 2176 4883 a Fv(L)p FL(\()p FB(B)s FL(\))p Black 0 4995 1560 4 v 92 5049 a Ff(1)127 5072 y SDict begin H.S end 127 5072 a 127 5072 a SDict begin H.R end 127 5072 a 127 5072 a SDict begin [/View [/XYZ H.V]/Dest (Hfootnote.1) cvn /DEST pdfmark end 127 5072 a FG(The)22 b(t)n(yp)r(e)g(of)f FR(3)551 5084 y Fe(X)652 5072 y FG(conforms)g(with)h(the)g(logical)i(reading)f(of)e FR(3)g FG(as)g Fd(\015)p FG(.)30 b(Indeed,)23 b FR(3)p FG(\()p Fc(x;)12 b(')p FG(\))21 b(&)g Fc(')f FR(\022)f Fc( )43 b FR(\))d(3)p FG(\()p Fc(x;)12 b( )r FG(\))22 b(and)g FR(3)p FG(\()p Fc(x;)11 b(')p FG(\))22 b(&)f Fc(x)e FR(\024)h Fc(y)42 b FR(\))0 5151 y(3)p FG(\()p Fc(y)r(;)12 b(')p FG(\),)24 b(where)g Fc(';)11 b( )26 b FG(are)e(upp)r(ersets)g(of)f Fb(X)17 b FG(.)p Black Black 1908 5400 a FL(25)p Black eop end end %%Page: 26 26 TeXDict begin HPSdict begin 26 25 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.26) cvn /DEST pdfmark end -8 -8 a Black Black 0 83 a FL(comm)n(utes)25 b(in)i FI(Pre)p FL(,)h(since)f Fv(y)g FL(is)g(natural.)35 b(Hence)28 b(the)g(square)1511 281 y FB(A)1597 250 y Fw(op)1917 280 y FA(\025)p 1699 261 225 4 v 1808 220 a FE(\()p Fn(y)1864 230 y Fo(A)1918 217 y Fm(op)1978 220 y FE(\))2004 228 y Fq(\005)2147 260 y Fy(/)p Fx(/)p 1923 261 V 1573 411 a FA(U)p 1591 418 4 113 v 1386 440 a FE(\()p Fz(f)1451 415 y Fm(op)1507 440 y FE(\))1533 448 y Fq(\005)1593 530 y Fy(\017)p Fx(\017)p 1591 530 V 2172 281 a Fv(L)p FL(\()p FB(A)19 b FL(\))2253 420 y FA(U)p 2271 426 4 100 v 2298 440 a FE(\()p Fn(L)p FE(\()p Fz(f)7 b FE(\)\))2480 448 y Fq(\005)2273 526 y Fy(\017)p Fx(\017)p 2271 526 V 1514 613 a FB(B)1592 583 y Fw(op)1917 612 y FA(\025)p 1696 594 228 4 v 1809 660 a FE(\()p Fn(y)1865 670 y Fo(B)1916 657 y Fm(op)1977 660 y FE(\))2003 668 y Fq(\005)2151 592 y Fy(/)p Fx(/)p 1923 594 V 2176 613 a Fv(L)p FL(\()p FB(B)s FL(\))0 815 y(comm)n(utes)25 b(in)i FI(Rel)o FL(\()p FI(Pre)q FL(\))h(since)e(\()p FK(\000)p FL(\))1140 827 y FJ(\005)1206 815 y FL(is)h(a)g(2-functor.) 125 914 y(No)n(w)f(observ)n(e)g(that)i Fv(L)p FL(\()p FF(f)9 b FL(\))23 b FK(a)g FL([)p FF(f)t(;)14 b Fv(2)p FL(])27 b(holds)f(b)n(y)h(the)h(de\014nition)e(of)h Fv(L)g FL(on)g(morphisms.)34 b(Hence)27 b(\()p Fv(L)p FL(\()p FF(f)9 b FL(\)\))3312 884 y FJ(\005)3374 914 y FK(a)23 b FL([)p FF(f)t(;)14 b Fv(2)p FL(])3622 884 y FJ(\005)3687 914 y FL(holds.)0 1014 y(Since)30 b(adjoin)n(ts)e(are)i(determined)e (uniquely)h(up)i(to)f(isomorphisms,)25 b(this)30 b(sho)n(ws)f(that)i (\()p Fv(L)p FL(\()p FF(f)9 b FL(\)\))3043 1026 y FJ(\005)3109 1014 y FL(=)28 b([)p FF(f)t(;)14 b Fv(2)p FL(])3376 984 y FJ(\005)3444 1014 y FL(\(w)n(e)31 b(use)f(that)0 1114 y(isomorphisms)22 b(are)27 b(iden)n(tities)e(in)i FI(Rel)o FL(\()p FI(Pre)q FL(\)\).)125 1213 y(Th)n(us,)j(taking)f(righ)n(t)g (adjoin)n(ts)g(ev)n(erywhere)f(in)i(the)h(ab)r(o)n(v)n(e)e(square)g(w)n (e)h(obtain)f(the)h(square)f(from)g(the)i(claim)c(of)k(the)0 1313 y(lemma.)p 3839 1313 4 57 v 3843 1260 50 4 v 3843 1313 V 3893 1313 4 57 v Black 0 1471 a FC(Computational)g(Pr)l(o)l(of.) p Black 43 w FL(By)d(de\014nition)962 1627 y FK(3)1017 1639 y Ft(A)1105 1627 y FK(\001)19 b FL([)p FF(f)t(;)14 b Fv(2)p FL(])1321 1593 y FJ(\005)1359 1627 y FL(\()p FF(a;)g(V)19 b FL(\))83 b(=)1802 1548 y Fu(_)1812 1727 y Fz(W)1908 1627 y FK(3)1963 1639 y Ft(A)2033 1627 y FL(\()p FF(a;)14 b(W)e FL(\))19 b FK(^)f FL([)p FB(A)h FF(;)14 b Fv(2)p FL(]\()p FF(V)38 b FK(\001)18 b FF(f)t(;)c(W)e FL(\))1654 1830 y(=)83 b FK(3)1857 1842 y Ft(A)1927 1830 y FL(\()p FF(a;)14 b(V)37 b FK(\001)19 b FF(f)9 b FL(\))1654 1955 y(=)83 b(\()p FF(V)37 b FK(\001)19 b FF(f)9 b FL(\)\()p FF(a)p FL(\))0 2099 y(where)27 b(the)h(second)f(step)h(is)e(due)i(to)g (the)g(Y)-7 b(oneda)27 b(Lemma.)34 b(Analogously:)1030 2255 y(\()p FF(f)1112 2221 y Fw(op)1190 2255 y FL(\))1222 2221 y FJ(\005)1279 2255 y FK(\001)18 b(3)1375 2267 y Ft(B)1440 2255 y FL(\()p FF(a;)c(V)19 b FL(\))83 b(=)1883 2176 y Fu(_)1914 2355 y Fz(b)1989 2255 y FB(B)2067 2221 y Fw(op)2145 2255 y FL(\()p FF(f)2227 2221 y Fw(op)2305 2255 y FF(a;)14 b(b)p FL(\))k FK(^)h(3)2601 2267 y Ft(B)2666 2255 y FL(\()p FF(b;)14 b(V)k FL(\))1735 2459 y(=)83 b FK(3)1938 2471 y Ft(B)2003 2459 y FL(\()p FF(f)9 b(a;)14 b(V)k FL(\))1735 2583 y(=)83 b FF(V)19 b FL(\()p FF(f)9 b(a)p FL(\))p 3839 2727 V 3843 2675 50 4 v 3843 2727 V 3893 2727 4 57 v 0 2886 a SDict begin H.S end 0 2886 a 0 2886 a SDict begin 12 H.A end 0 2886 a 0 2886 a SDict begin [/View [/XYZ H.V]/Dest (theorem.7.2) cvn /DEST pdfmark end 0 2886 a Black FM(Corollary)37 b(7.2.)p Black 43 w FC(F)-6 b(or)33 b(every)h(lo)l(c)l(al)t(ly)h(monotone)e(functor)g FF(T)45 b FC(that)33 b(satis\014es)g(the)g(Be)l(ck-Cheval)t(ley)k (Condition)d(and)g(for)0 2985 y(every)d(monotone)f(map)g FF(f)i FL(:)23 b FB(A)42 b FK(\000)-15 b(!)23 b FB(B)s FC(,)31 b(we)f(have)p 1429 3121 61 4 v 1429 3188 a FF(T)11 b FL([)p FB(A)19 b FF(;)14 b Fv(2)p FL(])1947 3187 y FA(\025)p 1729 3168 225 4 v 1878 3085 49 3 v 1878 3133 a Fz(T)9 b FJ(3)1971 3142 y Fo(A)2177 3167 y Fy(/)p Fx(/)p 1953 3168 225 4 v 2202 3121 61 4 v 2202 3188 a FF(T)i FB(A)2348 3157 y Fw(op)p 1433 3398 V 1433 3464 a FF(T)g FL([)p FB(B)s FF(;)j Fv(2)p FL(])1947 3463 y FA(\025)p 1726 3445 228 4 v 1879 3474 49 3 v 1879 3522 a Fz(T)9 b FJ(3)1972 3531 y Fo(B)2181 3443 y Fy(/)p Fx(/)p 1953 3445 228 4 v 1547 3293 a FA(U)p 1565 3366 4 67 v 1301 3271 49 3 v 1301 3319 a Fz(T)g FE([)p Fz(f)s(;)p Fn(2)p FE(])1478 3294 y Fq(\005)1567 3233 y Fy(O)p Fx(O)p 1565 3300 4 67 v 2206 3398 61 4 v 2206 3464 a FF(T)i FB(B)2344 3434 y Fw(op)2294 3283 y FA(U)p 2312 3366 4 77 v 2369 3261 49 3 v 2369 3309 a Fz(T)e FE(\()p Fz(f)2482 3284 y Fm(op)2538 3309 y FE(\))2564 3284 y Fq(\005)2314 3212 y Fy(O)p Fx(O)p 2312 3289 4 77 v 0 3667 a FL(Coming)25 b(bac)n(k)i(to)g FF(\016)f FL(:)d FF(LP)35 b FK(\000)-14 b(!)23 b FF(P)12 b(T)1141 3636 y Fw(op)1217 3667 y FL(.)37 b(It)28 b(su\016ces,)f(due)h(to)g FF(F)35 b FK(a)23 b FF(U)9 b FL(,)27 b(to)g(giv)n(e)1552 3811 y FF(\034)32 b FL(:)23 b FF(T)1727 3776 y Fz(@)1770 3811 y FF(U)9 b(P)34 b FK(\000)-14 b(!)23 b FF(U)9 b(P)j(T)2272 3776 y Fw(op)0 3955 y FL(Observ)n(e)26 b(that,)i(for)f(ev)n(ery)f(preorder)g FB(X)c FL(,)28 b(w)n(e)f(ha)n(v)n(e)1192 4099 y FF(U)9 b(P)j(T)1384 4064 y Fw(op)1460 4099 y FL(\()p FB(X)22 b FL(\))i(=)e([)p FF(T)1819 4064 y Fw(op)1896 4099 y FB(X)g FF(;)14 b Fv(2)p FL(])23 b(=)g Fv(L)p FL(\(\()p FF(T)2389 4064 y Fw(op)2466 4099 y FB(X)f FL(\))2598 4064 y Fw(op)2676 4099 y FL(\))0 4243 y(By)31 b(Prop)r(osition)584 4243 y SDict begin H.S end 584 4243 a Black FL(2.7)p Black 690 4189 a SDict begin H.R end 690 4189 a 690 4243 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.2.7) cvn H.B /ANN pdfmark end 690 4243 a FL(,)h(to)f(de\014ne)h FF(\034)1130 4255 y Ft(X)1242 4243 y FL(it)f(su\016ces)f(to)h(giv)n(e)e(a)i (relation)d(from)i FF(T)2535 4213 y Fz(@)2577 4243 y FF(U)9 b(P)j FB(X)53 b FL(to)31 b(\()p FF(T)3037 4213 y Fw(op)3114 4243 y FB(X)22 b FL(\))3246 4213 y Fw(op)3324 4243 y FL(,)32 b(and)f(w)n(e)f(obtain)0 4353 y(it)38 b(from)g(Theorem)664 4353 y SDict begin H.S end 664 4353 a Black FL(5.3)p Black 770 4299 a SDict begin H.R end 770 4299 a 770 4353 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.5.3) cvn H.B /ANN pdfmark end 770 4353 a 38 w FL(b)n(y)h(applying)p 1285 4279 104 4 v 36 w FF(T)1346 4329 y Fz(@)1427 4353 y FL(to)g(the)g(relation)d FK(3)2065 4365 y Ft(X)2146 4353 y FL(.)71 b(That)39 b FF(\034)2495 4365 y Ft(X)2615 4353 y FL(so)f(de\014ned)h(is)f(natural,)i(follo)n(ws) 35 b(from)0 4452 y(Corollary)367 4452 y SDict begin H.S end 367 4452 a Black FL(7.2)p Black 473 4399 a SDict begin H.R end 473 4399 a 473 4452 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.7.2) cvn H.B /ANN pdfmark end 473 4452 a FL(.)i(This)27 b(follo)n(ws)d([)1018 4452 y SDict begin H.S end 1018 4452 a Black FL(KKuV)p Black 1256 4396 a SDict begin H.R end 1256 4396 a 1256 4452 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kkv:aiml08) cvn H.B /ANN pdfmark end 1256 4452 a FL(])k(with)f(the)h(exception)e(that)i(here)f(no)n (w)g(w)n(e)g(need)h(to)f(use)h FF(T)3165 4422 y Fz(@)3207 4452 y FL(.)0 4588 y SDict begin H.S end 0 4588 a 0 4588 a SDict begin 12 H.A end 0 4588 a 0 4588 a SDict begin [/View [/XYZ H.V]/Dest (theorem.7.3) cvn /DEST pdfmark end 0 4588 a Black FM(Example)36 b(7.3.)p Black 42 w FL(Recall)30 b(the)j(functor)f Fv(P)1341 4557 y Fz(c)1341 4608 y(!)1422 4588 y FL(of)g(Example)1870 4588 y SDict begin H.S end 1870 4588 a Black FL(6.4)p Black 1976 4534 a SDict begin H.R end 1976 4534 a 1976 4588 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.6.4) cvn H.B /ANN pdfmark end 1976 4588 a 33 w FL(and)g(consider)e(a)i(coalgebra)d FF(c)h FL(:)h FB(X)53 b FK(\000)-14 b(!)31 b Fv(P)3420 4557 y Fz(c)3420 4608 y(!)3468 4588 y FB(X)22 b FL(.)51 b(On)32 b(the)0 4687 y(logical)26 b(side)j(w)n(e)h(allo)n(w)e(ourselv)n(es)f (to)j(write)f FK(r)p FF(\013)i FL(for)f(an)n(y)g(\014nite)g(subset)g FF(\013)h FL(of)f FF(U)9 b FL(\()p FK(L)p FL(\).)46 b(Of)31 b(course,)e(w)n(e)h(then)h(ha)n(v)n(e)e(to)i(b)r(e)0 4787 y(careful)f(that)i(the)g(seman)n(tics)d(of)j FF(\013)g FL(agrees)e(with)i(the)g(seman)n(tics)d(of)i(the)i(con)n(v)n(ex)d (closure)f(of)j FF(\013)p FL(.)50 b(In)n(terestingly)-7 b(,)30 b(this)h(is)0 4886 y(done)25 b(automatically)20 b(b)n(y)25 b(the)h(mac)n(hinery)c(set)j(up)h(in)e(the)i(previous)d (section,)h(since)g Fv(P)2730 4856 y Fz(c)2730 4907 y(!)2801 4886 y FL(=)f FF(Q)p Fv(P)3008 4898 y Fz(!)3056 4886 y FF(I)32 b FL(and)25 b(all)e(these)i(functors)0 4986 y(are)i(self-dual.)34 b(By)27 b(Example)976 4986 y SDict begin H.S end 976 4986 a Black FL(6.6)p Black 1082 4933 a SDict begin H.R end 1082 4933 a 1082 4986 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (theorem.6.6) cvn H.B /ANN pdfmark end 1082 4986 a FL(,)h(the)g(seman)n(tics)d(of)i FK(r)p FF(\013)i FL(is)d(giv)n(en)g(b)n(y)723 5130 y FF(x)d FD(\015)g FK(r)p FF(\013)107 b FK(,)f(8)p FF(y)25 b FK(2)e FF(c)p FL(\()p FF(x)p FL(\))p FK(9)p FF(')i FK(2)e FF(\013:y)j FD(\015)d FF(')56 b FL(and)28 b FK(8)p FF(')22 b FK(2)h FF(\013)p FK(9)p FF(y)k FK(2)c FF(c)p FL(\()p FF(x)p FL(\))p FF(:y)k FD(\015)c FF(':)p Black 1908 5400 a FL(26)p Black eop end end %%Page: 27 27 TeXDict begin HPSdict begin 27 26 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.27) cvn /DEST pdfmark end -8 -8 a Black Black 0 0 a SDict begin H.S end 0 0 a 0 0 a SDict begin 12 H.A end 0 0 a 0 0 a SDict begin [/View [/XYZ H.V]/Dest (section.8) cvn /DEST pdfmark end 0 0 a 83 x FN(8)135 b(Conclusions)0 265 y FL(W)-7 b(e)32 b(hop)r(e)g(to)g(ha)n(v)n(e)f(illustrated)e(in)i (the)h(previous)e(t)n(w)n(o)h(sections)g(that,)i(after)f(getting)e (used)i(to)g(handle)f(the)h(\()p FK(\000)p FL(\))3657 277 y FJ(\005)3696 265 y FF(;)14 b FL(\()p FK(\000)p FL(\))3862 235 y FJ(\005)0 364 y FL(and)37 b(\()p FK(\000)p FL(\))300 334 y Fw(op)377 364 y FL(,)j(the)d(tec)n(hniques)f(dev)n (elop)r(ed)f(here)h(w)n(ork)g(surprisingly)c(smo)r(othly)i(and)j(will)d (b)r(e)j(useful)f(in)g(man)n(y)g(future)0 464 y(dev)n(elopmen)n(ts.)42 b(F)-7 b(or)30 b(example,)f(an)h(observ)-5 b(ation)28 b(crucial)g(for)h(b)r(oth)i([)2243 464 y SDict begin H.S end 2243 464 a Black FL(KKuV)p Black 2481 407 a SDict begin H.R end 2481 407 a 2481 464 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kkv:aiml08) cvn H.B /ANN pdfmark end 2481 464 a FL(,)2534 464 y SDict begin H.S end 2534 464 a Black FL(KuL)p Black 2697 407 a SDict begin H.R end 2697 407 a 2697 464 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kurz-leal:mfps09) cvn H.B /ANN pdfmark end 2697 464 a FL(])f(is)g(that)g(comp)r (osing)e(the)j(singleton)0 564 y(map)h FF(X)37 b FK(\000)-14 b(!)31 b FB(P)7 b FF(X)g FL(,)33 b FF(x)f FK(7!)g(f)p FF(x)p FK(g)p FL(,)h(with)f(the)h(relation)38 b FK(3)1780 576 y Fz(X)1844 564 y FL(:)23 b FB(P)7 b FF(X)2158 563 y FA(\025)p 2064 545 100 4 v 2264 543 a Fy(/)p Fx(/)p 2164 545 V 2272 564 a FF(X)47 b FL(is)32 b FC(id)2553 576 y Fz(X)2616 564 y FL(.)52 b(Referring)31 b(bac)n(k)h(to)g(\()3397 564 y SDict begin H.S end 3397 564 a Black FL(7.19)p Black 3545 510 a SDict begin H.R end 3545 510 a 3545 564 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.7.19) cvn H.B /ANN pdfmark end 3545 564 a FL(\),)i(w)n(e)f(\014nd)0 663 y(here)27 b(the)h(same)e(relationship)1194 763 y FK(3)1250 775 y Ft(A)1338 763 y FK(\016)18 b FL(\()p Fv(y)1469 775 y Ft(A)1535 759 y Fm(op)1596 763 y FL(\))1628 775 y FJ(\005)1689 763 y FL(=)23 b(\()p Fv(y)1848 775 y Ft(A)1914 759 y Fm(op)1975 763 y FL(\))2007 729 y FJ(\005)2064 763 y FK(\016)18 b FL(\()p Fv(y)2195 775 y Ft(A)2261 759 y Fm(op)2322 763 y FL(\))2354 775 y FJ(\005)2415 763 y FL(=)23 b FC(id)2579 775 y Ft(A)2645 759 y Fm(op)0 912 y FL(The)38 b(question)f(whether)h(the)g(completeness)e(pro)r(of)i (of)g([)1870 912 y SDict begin H.S end 1870 912 a Black FL(KKuV)p Black 2107 856 a SDict begin H.R end 2107 856 a 2107 912 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kkv:aiml08) cvn H.B /ANN pdfmark end 2107 912 a FL(])h(and)f(the)g(relationship) c(b)r(et)n(w)n(een)k FK(r)h FL(and)f(predicate)0 1012 y(liftings)25 b(of)i([)392 1012 y SDict begin H.S end 392 1012 a Black FL(KuL)p Black 555 955 a SDict begin H.R end 555 955 a 555 1012 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kurz-leal:mfps09) cvn H.B /ANN pdfmark end 555 1012 a FL(])h(can)f(b)r(e)h (carried)d(o)n(v)n(er)h(to)i(our)e(setting)h(are)g(a)g(direction)e(of)i (future)h(researc)n(h.)125 1112 y(Another)22 b(direction)f(is)g(the)i (generalisation)18 b(to)23 b(categories)d(whic)n(h)h(are)h(enric)n(hed) f(o)n(v)n(er)g(more)g(general)g(structures)h(than)0 1211 y Fv(2)p FL(,)27 b(suc)n(h)g(as)f(comm)n(utativ)n(e)d(quan)n(tales.)35 b(Sim)n(ulation,)23 b(relation)h(lifting)g(and)j(\014nal)e(coalgebras)f (in)i(this)g(setting)g(ha)n(v)n(e)g(b)r(een)0 1311 y(studied)h(in)g([) 411 1311 y SDict begin H.S end 411 1311 a Black FL(W)-7 b(o)p Black 531 1254 a SDict begin H.R end 531 1254 a 531 1311 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.worrell:cmcs00) cvn H.B /ANN pdfmark end 531 1311 a FL(].)0 1585 y SDict begin H.S end 0 1585 a 0 1585 a SDict begin 18 H.A end 0 1585 a 0 1585 a SDict begin [/View [/XYZ H.V]/Dest (section*.2) cvn /DEST pdfmark end 0 1585 a FN(References)p Black 0 1767 a SDict begin H.S end 0 1767 a FL([ABSV])275 1767 y SDict begin 12 H.A end 275 1767 a 275 1767 a SDict begin [/View [/XYZ H.V]/Dest (cite.absv) cvn /DEST pdfmark end 275 1767 a Black 117 w FL(J.)21 b(Ad\023)-42 b(amek,)22 b(R.)g(El)e(Bashir,)g(M.)i(Sobral)d(and)j(J.)f(V)-7 b(elebil,)20 b(On)h(functors)g(that)h(are)e(lax)g(epimorphisms,)e FC(The)l(ory)392 1867 y(Appl.)31 b(Cate)l(g.)e FL(8.20)d(\(2001\),)g (509{521.)p Black 0 2033 a SDict begin H.S end 0 2033 a FL([BK])170 2033 y SDict begin 12 H.A end 170 2033 a 170 2033 a SDict begin [/View [/XYZ H.V]/Dest (cite.bala-kurz:calco11) cvn /DEST pdfmark end 170 2033 a Black 222 w FL(A.)32 b(Balan)d(and)j(A.)f(Kurz,)h(Finitary)d(F)-7 b(unctors:)44 b(from)30 b FI(Set)i FL(to)f FI(Preo)n(rd)g FL(and)h FI(P)n(oset)p FL(,)f FC(T)-6 b(o)34 b(app)l(e)l(ar)g(in)g(CALCO)392 2133 y(\(2011\))p Black 0 2299 a SDict begin H.S end 0 2299 a FL([Bal])171 2299 y SDict begin 12 H.A end 171 2299 a 171 2299 a SDict begin [/View [/XYZ H.V]/Dest (cite.baltag:cmcs00) cvn /DEST pdfmark end 171 2299 a Black 221 w FL(A.)j(Baltag,)f (A)h(logic)d(for)i(coalgebraic)c(sim)n(ulation,)i FC(Ele)l(ctr)l(on.)k (Notes)g(The)l(or.)i(Comput.)e(Sci.)g FL(33)d(\(2000\),)392 2398 y(41{60.)p Black 0 2564 a SDict begin H.S end 0 2564 a FL([Ba])147 2564 y SDict begin 12 H.A end 147 2564 a 147 2564 a SDict begin [/View [/XYZ H.V]/Dest (cite.barr:rel-alg) cvn /DEST pdfmark end 147 2564 a Black 245 w FL(M.)27 b(Barr,)e(Relational)d(algebras,)i(in:)35 b FC(R)l(ep)l(orts)28 b(of)i(the)e(Midwest)i(Cate)l(gory)g(Seminar)f(IV)15 b FL(,)26 b(Lecture)g(Notes)g(in)392 2664 y(Mathematics)f(137,)i (Springer)e(1970,)h(39{55.)p Black 0 2830 a SDict begin H.S end 0 2830 a FL([BV])167 2830 y SDict begin 12 H.A end 167 2830 a 167 2830 a SDict begin [/View [/XYZ H.V]/Dest (cite.bv) cvn /DEST pdfmark end 167 2830 a Black 225 w FL(R.)h(El)f(Bashir)f(and)i(J.)f(V)-7 b(elebil,)25 b(Re\015ectiv)n(e)h(and)h(core\015ectiv)n(e)d(sub)r(categories)g(of)j (preshea)n(v)n(es,)e FC(The)l(ory)31 b(Appl.)392 2930 y(Cate)l(g.)e FL(10.16)d(\(2002\),)g(410{423.)p Black 0 3096 a SDict begin H.S end 0 3096 a FL([CKW])256 3096 y SDict begin 12 H.A end 256 3096 a 256 3096 a SDict begin [/View [/XYZ H.V]/Dest (cite.ckw:wpb) cvn /DEST pdfmark end 256 3096 a Black 136 w FL(A.)20 b(Carb)r(oni,)f(G.)g(M.)h(Kelly) c(and)j(R.)h(J.)f(W)-7 b(o)r(o)r(d,)21 b(A)e(2-categorical)14 b(approac)n(h)k(to)h(c)n(hange)f(of)h(base)f(and)h(geometric)392 3195 y(morphisms)24 b(I,)k FC(Cahiers)j(de)g(T)-6 b(op.)31 b(et)e(G)n(\023)-40 b(eom.)31 b(Di\013.)d FL(XXXI)r(I.1)h(\(1991\),)d (47{95.)p Black 0 3361 a SDict begin H.S end 0 3361 a FL([Gu])157 3361 y SDict begin 12 H.A end 157 3361 a 157 3361 a SDict begin [/View [/XYZ H.V]/Dest (cite.guitart) cvn /DEST pdfmark end 157 3361 a Black 235 w FL(R.)i(Guitart,)f (Relations)e(et)i(carr)n(\023)-39 b(es)25 b(exacts,)i FC(A)n(nn.)i(Sci.)i(Math.)g(Qu)n(\023)-40 b(eb)l(e)l(c)32 b FL(IV.2)27 b(\(1980\),)f(103{125.)p Black 0 3527 a SDict begin H.S end 0 3527 a FL([He])145 3527 y SDict begin 12 H.A end 145 3527 a 145 3527 a SDict begin [/View [/XYZ H.V]/Dest (cite.hermida) cvn /DEST pdfmark end 145 3527 a Black 247 w FL(C.)67 b(Hermida,)74 b(A)67 b(categorical)c(outlo) r(ok)h(on)j(relational)62 b(mo)r(dalities)h(and)j(sim)n(ulations,)72 b FC(pr)l(eprint,)392 3645 y SDict begin H.S end 392 3645 a Black -18 x Fa (http://maggie.cs)o(.qu)o(ee)o(nsu)o(.c)o(a/)o(che)o(rm)o(ida)o(/p)o (ap)o(ers)o(/s)o(at-)s(sim)o(-)t(I)o(and)o(C.)o(pdf)p Black 3059 3569 a SDict begin H.R end 3059 3569 a 3059 3627 a SDict begin [/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Color [0 1 1]/Action <</Subtype/URI/URI(http://maggie.cs.queensu.ca/chermida/papers/sat-sim-IandC.pdf)>>/Subtype /Link H.B /ANN pdfmark end 3059 3627 a FL(.)p Black 0 3793 a SDict begin H.S end 0 3793 a FL([HeJ])188 3793 y SDict begin 12 H.A end 188 3793 a 188 3793 a SDict begin [/View [/XYZ H.V]/Dest (cite.herm-jaco:pred-lift) cvn /DEST pdfmark end 188 3793 a Black 204 w FL(C.)33 b(Hermida)e(and)i(B.) g(Jacobs,)g(Structural)f(induction)f(and)i(coinduction)e(in)i(the)g (\014brational)d(setting,)k FC(In-)392 3893 y(form.)d(and)f(Comput.)f FL(145)d(\(1998\),)g(107{152.)p Black 0 4059 a SDict begin H.S end 0 4059 a FL([HuJ])197 4059 y SDict begin 12 H.A end 197 4059 a 197 4059 a SDict begin [/View [/XYZ H.V]/Dest (cite.hugh-jaco:simulation) cvn /DEST pdfmark end 197 4059 a Black 195 w FL(J.)h(Hughes)h(and)f(B.)h(Jacobs,)e(Sim)n(ulations)d (in)k(coalgebra.)d(Theor.)j(Comput.)g(Sci.)g(327)f(\(2004\),)g(71{108.) p Black 0 4225 a SDict begin H.S end 0 4225 a FL([KaKuV])326 4225 y SDict begin 12 H.A end 326 4225 a 326 4225 a SDict begin [/View [/XYZ H.V]/Dest (cite.kkv:expr) cvn /DEST pdfmark end 326 4225 a Black 66 w FL(K.)i(Kapulkin,)e(A.)i(Kurz,)g(J.) g(V)-7 b(elebil,)26 b(Expressivit)n(y)e(of)k(Coalgebraic)c(Logic)i(o)n (v)n(er)g(P)n(osets,)h(in:)38 b(CMCS)28 b(2010)392 4324 y(Short)f(con)n(tributions,)e(CWI)j(T)-7 b(ec)n(hnical)25 b(rep)r(ort)i(SEN-1004,)e(pp.)j(16{17)d(\(2010\))p Black 0 4490 a SDict begin H.S end 0 4490 a FL([Ke])148 4490 y SDict begin 12 H.A end 148 4490 a 148 4490 a SDict begin [/View [/XYZ H.V]/Dest (cite.kelly:book) cvn /DEST pdfmark end 148 4490 a Black 244 w FL(G.)h(M.)h(Kelly)-7 b(,)24 b FC(Basic)29 b(c)l(onc)l(epts)g(of)g(enriche)l(d)g(c)l(ate)l(gory)h (the)l(ory)p FL(,)d(London)e(Math.)h(So)r(c.)g(Lecture)g(Notes)g (Series)392 4590 y(64,)h(Cam)n(bridge)d(Univ.)j(Press,)f(1982.)p Black 0 4756 a SDict begin H.S end 0 4756 a FL([Kl])135 4756 y SDict begin 12 H.A end 135 4756 a 135 4756 a SDict begin [/View [/XYZ H.V]/Dest (cite.klin:thesis) cvn /DEST pdfmark end 135 4756 a Black 257 w FL(B.)c(Klin,)f(An)i(Abstract)e (Coalgebraic)d(Approac)n(h)j(to)h(Pro)r(cess)e(Equiv)-5 b(alence)19 b(for)j(W)-7 b(ell-Beha)n(v)n(ed)19 b(Op)r(erational)392 4856 y(Seman)n(tics.)25 b(Univ)n(ersit)n(y)g(of)j(Aarh)n(us,)e(2004.)p Black 0 5022 a SDict begin H.S end 0 5022 a FL([KKuV])284 5022 y SDict begin 12 H.A end 284 5022 a 284 5022 a SDict begin [/View [/XYZ H.V]/Dest (cite.kkv:aiml08) cvn /DEST pdfmark end 284 5022 a Black 108 w FL(C.)36 b(Kupk)n(e,)h(A.)f(Kurz)f (and)g(Y.)h(V)-7 b(enema,)37 b(Completeness)c(of)j(the)g(\014nitary)e (Moss)h(logic,)g(in:)52 b FC(A)l(dvanc)l(es)38 b(in)392 5121 y(Mo)l(dal)31 b(L)l(o)l(gic)g(2008)p FL(,)e(College)c (Publications,)f(193{217)p Black 1908 5400 a(27)p Black eop end end %%Page: 28 28 TeXDict begin HPSdict begin 28 27 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.28) cvn /DEST pdfmark end -8 -8 a Black Black Black 0 83 a SDict begin H.S end 0 83 a FL([KuL])209 83 y SDict begin 12 H.A end 209 83 a 209 83 a SDict begin [/View [/XYZ H.V]/Dest (cite.kurz-leal:mfps09) cvn /DEST pdfmark end 209 83 a Black 183 w FL(A.)40 b(Kurz)f(and)g(R.)h(Leal,)i(Equational) 36 b(coalgebraic)f(logic,)40 b FC(Ele)l(ctr)l(on.)h(Notes)g(The)l(or.)h (Comput.)g(Sci.)e FL(249)392 183 y(\(2009\),)26 b(333{356.)p Black 0 349 a SDict begin H.S end 0 349 a FL([L])98 349 y SDict begin 12 H.A end 98 349 a 98 349 a SDict begin [/View [/XYZ H.V]/Dest (cite.levy:simulation) cvn /DEST pdfmark end 98 349 a Black 294 w FL(P)-7 b(.)29 b(Levy)-7 b(,)29 b(Similarit)n(y)24 b(quotien)n(ts)k(as)h(\014nal)f(coalgebras,)e(in:)40 b FC(F)-6 b(oSSaCS)31 b(2011)p FL(,)h(Lecture)d(Notes)g(in)f(Computer) 392 448 y(Science)f(6604,)e(Springer)h(2011.)p Black 0 614 a SDict begin H.S end 0 614 a FL([M)99 626 y FE(1)136 614 y FL(])159 614 y SDict begin 12 H.A end 159 614 a 159 614 a SDict begin [/View [/XYZ H.V]/Dest (cite.marmolejo1) cvn /DEST pdfmark end 159 614 a Black 233 w FL(F.)e(Marmolejo,)d (Do)r(ctrines)i(whose)g(structure)g(forms)f(a)i(fully)e(faithful)g (adjoin)n(t)h(string,)g FC(The)l(or.)28 b(Appl.)f(Cate)l(g.)392 714 y FL(3:2)g(\(1997\),)f(24{44.)p Black 0 880 a SDict begin H.S end 0 880 a FL([M)99 892 y FE(2)136 880 y FL(])159 880 y SDict begin 12 H.A end 159 880 a 159 880 a SDict begin [/View [/XYZ H.V]/Dest (cite.marmolejo2) cvn /DEST pdfmark end 159 880 a Black 233 w FL(F.)i(Marmolejo,)c(Distributiv)n(e) h(la)n(ws)h(for)h(pseudomonads,)e FC(The)l(or.)32 b(Appl.)f(Cate)l(g.)d FL(5:5)f(\(1999\),)f(91{147.)p Black 0 1046 a SDict begin H.S end 0 1046 a FL([MR)-9 b(W])259 1046 y SDict begin 12 H.A end 259 1046 a 259 1046 a SDict begin [/View [/XYZ H.V]/Dest (cite.marmolejo+rosebrugh+wood) cvn /DEST pdfmark end 259 1046 a Black 133 w FL(F.)26 b(Marmolejo,)d(R.)j(Rosebrugh)e(and)h(R.)h (J.)f(W)-7 b(o)r(o)r(d,)27 b(Dualit)n(y)c(for)i(CCD)h(lattices,)e FC(The)l(or.)30 b(Appl.)f(Cate)l(g.)d FL(22:1)392 1146 y(\(2009\),)g(1{23.)p Black 0 1312 a SDict begin H.S end 0 1312 a FL([Mo])164 1312 y SDict begin 12 H.A end 164 1312 a 164 1312 a SDict begin [/View [/XYZ H.V]/Dest (cite.moss:cl) cvn /DEST pdfmark end 164 1312 a Black 228 w FL(L.)i(Moss,)f (Coalgebraic)c(logic,)i FC(A)n(nn.)k(Pur)l(e)g(Appl.)i(L)l(o)l(gic)i FL(96)27 b(\(1999\),)f(277{317)p Black 0 1478 a SDict begin H.S end 0 1478 a FL([R])107 1478 y SDict begin 12 H.A end 107 1478 a 107 1478 a SDict begin [/View [/XYZ H.V]/Dest (cite.rutten-rel) cvn /DEST pdfmark end 107 1478 a Black 285 w FL(J.)d(Rutten,)h(Relators)d(and)i(Metric)e(Bisim)n (ulations)c(\(Extended)23 b(Abstract\),)h FC(Ele)l(ctr.)i(Notes)f(The)l (or.)i(Comput.)392 1577 y(Sci.)i FL(11)d(\(1998\),)h(252{258.)p Black 0 1743 a SDict begin H.S end 0 1743 a FL([S)69 1755 y FE(1)106 1743 y FL(])129 1743 y SDict begin 12 H.A end 129 1743 a 129 1743 a SDict begin [/View [/XYZ H.V]/Dest (cite.street:monads) cvn /DEST pdfmark end 129 1743 a Black 263 w FL(R.)h(Street,)g(The)f(formal)e(theory)i(of)h(monads,)d FC(J.)30 b(Pur)l(e)g(Appl.)h(A)n(lgebr)l(a)j FL(2)27 b(\(1972\),)g(149{168.)p Black 0 1910 a SDict begin H.S end 0 1910 a FL([S)69 1922 y FE(2)106 1910 y FL(])129 1910 y SDict begin 12 H.A end 129 1910 a 129 1910 a SDict begin [/View [/XYZ H.V]/Dest (cite.street1) cvn /DEST pdfmark end 129 1910 a Black 263 w FL(R.)j(Street,)h(Fibrations)d(and)i(Y)-7 b(oneda's)30 b(lemma)d(in)i(a)h(2-category)-7 b(,)28 b(in:)41 b FC(Cate)l(gory)34 b(Seminar,)f(Sydney)g(1974)11 b FL(,)392 2009 y(Lecture)27 b(Notes)h(in)e(Mathematics)g(420,)g (Springer)g(1974,)f(104{133.)p Black 0 2175 a SDict begin H.S end 0 2175 a FL([S)69 2187 y FE(3)106 2175 y FL(])129 2175 y SDict begin 12 H.A end 129 2175 a 129 2175 a SDict begin [/View [/XYZ H.V]/Dest (cite.street2) cvn /DEST pdfmark end 129 2175 a Black 263 w FL(R.)34 b(Street,)h(Elemen)n (tary)30 b(cosmoi)h(I,)j(in:)48 b FC(Cate)l(gory)36 b(Seminar,)i (Sydney)e(1974)11 b FL(,)37 b(Lecture)c(Notes)h(in)e(Mathe-)392 2275 y(matics)25 b(420,)i(Springer)e(1974,)h(134{180.)p Black 0 2441 a SDict begin H.S end 0 2441 a FL([S)69 2453 y FE(4)106 2441 y FL(])129 2441 y SDict begin 12 H.A end 129 2441 a 129 2441 a SDict begin [/View [/XYZ H.V]/Dest (cite.street:fibrations) cvn /DEST pdfmark end 129 2441 a Black 263 w FL(R.)i(Street,)g(Fibrations)c(in)j(bicategories,)d FC(Cahiers)32 b(de)e(T)-6 b(op.)31 b(et)f(G)n(\023)-40 b(eom.)30 b(Di\013.)f FL(XXI.2)e(\(1980\),)g(111{159.)p Black 0 2607 a SDict begin H.S end 0 2607 a FL([V])108 2607 y SDict begin 12 H.A end 108 2607 a 108 2607 a SDict begin [/View [/XYZ H.V]/Dest (cite.venema:coalg-aut) cvn /DEST pdfmark end 108 2607 a Black 284 w FL(Y.)38 b(V)-7 b(enema,)38 b(Automata)e(and)h(\014xed)g(p)r(oin)n(t)g(logic:)53 b(a)37 b(coalgebraic)32 b(p)r(ersp)r(ectiv)n(e,)39 b FC(Inform.)g(and)g(Comput.)392 2707 y FL(204.4)26 b(\(2006\),)g (637{678.)p Black 0 2873 a SDict begin H.S end 0 2873 a FL([W)-7 b(o])166 2873 y SDict begin 12 H.A end 166 2873 a 166 2873 a SDict begin [/View [/XYZ H.V]/Dest (cite.worrell:cmcs00) cvn /DEST pdfmark end 166 2873 a Black 226 w FL(J.)30 b(W)-7 b(orrell,)27 b(Coinduction)h(for)h(recursiv)n(e)e(data)i(t)n(yp) r(es:)41 b(partial)27 b(orders,)i(metric)e(spaces)i(and)g (\012-categories.)392 2972 y FC(Ele)l(ctr)l(on.)h(Notes)g(The)l(or.)h (Comput.)g(Sci.)d FL(33)f(\(2000\),)f(337{356.)p Black 1908 5400 a(28)p Black eop end end %%Trailer end userdict /end-hook known{end-hook}if %%EOF