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</div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Emily Riehl</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Emily Riehl</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Emily_Riehl.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Emily_Riehl.jpg/220px-Emily_Riehl.jpg" decoding="async" width="220" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/34/Emily_Riehl.jpg 1.5x" data-file-width="257" data-file-height="266" /></a></span><div class="infobox-caption">Emily Riehl in 2014</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="birthplace"><a href="/wiki/Thousand_Oaks,_California" title="Thousand Oaks, California">Thousand Oaks</a>, California, US</div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a></li> <li><a href="/wiki/University_of_Cambridge" title="University of Cambridge">University of Cambridge</a></li> <li><a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a></li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a></li> <li><a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i> Algebraic model structures </i> <span style="font-size:97%;">(2011)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/J._Peter_May" title="J. Peter May">J. Peter May</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Emily Riehl</b> is an American <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> who has contributed to <a href="/wiki/Higher_category_theory" title="Higher category theory">higher category theory</a> and <a href="/wiki/Homotopy_theory" title="Homotopy theory">homotopy theory</a>. Much of her work, including her PhD thesis,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> concerns <a href="/wiki/Model_category" title="Model category">model structures</a> and more recently the foundations of <a href="/wiki/Infinity-categories" class="mw-redirect" title="Infinity-categories">infinity-categories</a>.<sup id="cite_ref-phdplus_2-0" class="reference"><a href="#cite_note-phdplus-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> She is the author of two textbooks<sup id="cite_ref-AMS_4-0" class="reference"><a href="#cite_note-AMS-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-baez_5-0" class="reference"><a href="#cite_note-baez-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and serves on the editorial boards of three journals.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Education_and_career">Education and career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=1" title="Edit section: Education and career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Riehl grew up in <a href="/wiki/Bloomington-Normal,_Illinois" class="mw-redirect" title="Bloomington-Normal, Illinois">Bloomington-Normal</a>, Illinois.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> As a high school student at <a href="/wiki/University_High_School_(Normal,_Illinois)" title="University High School (Normal, Illinois)">University High School</a> in Normal in 2002, she won third place in the national <a href="/wiki/Intel_Science_Talent_Search" class="mw-redirect" title="Intel Science Talent Search">Intel Science Talent Search</a> for a project in mathematics entitled "On the Properties of Tits Graphs".<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Riehl attended <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a> as an undergraduate; with <a href="/wiki/Benedict_Gross" title="Benedict Gross">Benedict Gross</a> as a mentor, she wrote a senior thesis on <a href="/wiki/Local_class_field_theory" title="Local class field theory">local class field theory</a>. She also headed the school <a href="/wiki/Rugby_football" title="Rugby football">rugby</a> team and played viola in the Harvard–Radcliffe Orchestra.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> After Harvard, she completed <a href="/wiki/Part_III_of_the_Mathematical_Tripos" title="Part III of the Mathematical Tripos">part III of the Maths Tripos at Cambridge</a>.<sup id="cite_ref-AMS_4-1" class="reference"><a href="#cite_note-AMS-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> She defended her doctoral dissertation, <i>Algebraic model structures</i>, at the <a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a> in 2011, supervised by <a href="/wiki/J._Peter_May" title="J. Peter May">J. Peter May</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Between 2011 and 2015, Riehl held a position at Harvard University as a Benjamin Peirce Postdoctoral Fellow. Since 2015, she has been employed at <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a>, where she became an <a href="/wiki/Associate_professor" title="Associate professor">associate professor</a> in 2019. In addition, she teaches on <a href="/wiki/EdX" title="EdX">edX</a> and has hosted videos for <a href="/wiki/Numberphile" title="Numberphile">Numberphile</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Along with Benedict Gross and Joe Harris, she developed a Harvard course on edX titled "Fat Chance: Probability from the Ground Up".<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Honors_and_awards">Honors and awards</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=2" title="Edit section: Honors and awards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In January 2020, Riehl received the JHU President's Frontier Award, a $250,000 award that "supports individuals at Johns Hopkins who are breaking new ground and poised to become leaders in their field". She is the sixth JHU faculty member to receive the award.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Riehl was awarded the 2021 AWM <a href="/wiki/Joan_%26_Joseph_Birman_Research_Prize_in_Topology_and_Geometry" title="Joan & Joseph Birman Research Prize in Topology and Geometry">Joan & Joseph Birman Research Prize</a> "for her deep and foundational work in category theory and homotopy theory."<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> She is the fourth winner of this prize. She was named a Fellow of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>, in the 2022 class of fellows, "for contributions to research, exposition, and communication in higher category theory".<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In 2022 she was awarded a <a href="/wiki/Simons_Foundation" title="Simons Foundation">Simons</a> Fellowship.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Service_and_outreach">Service and outreach</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=3" title="Edit section: Service and outreach"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Riehl is a host of the n-Category Café, a blog on subjects related to category theory in mathematics, physics, and philosophy.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> She was a board member of the LGBT mathematical association <a href="/wiki/Spectra_(mathematical_association)" title="Spectra (mathematical association)">Spectra</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Other_activities">Other activities</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=4" title="Edit section: Other activities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In addition to her mathematical work, Riehl has competed on the <a href="/wiki/United_States_women%27s_national_Australian_rules_football_team" title="United States women's national Australian rules football team">United States women's national Australian rules football team</a> at the <a href="/wiki/Australian_Football_International_Cup" title="Australian Football International Cup">Australian Football International Cup</a>,<sup id="cite_ref-phdplus_2-1" class="reference"><a href="#cite_note-phdplus-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> and was vice captain of the team at the 2017 cup.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>While working as a postdoctoral researcher at Harvard, she played <a href="/wiki/Electric_bass" class="mw-redirect" title="Electric bass">electric bass</a> in the band Unstraight.<sup id="cite_ref-phdplus_2-2" class="reference"><a href="#cite_note-phdplus-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> She has also written about "unstraightening" in her mathematical research.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Books">Books</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=5" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Riehl is the author of three books, with a fourth in preparation: </p> <ul><li><i>Categorical Homotopy Theory</i> (2014)<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li> <li><i>Category Theory in Context</i> (2016)<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Fat_Chance:_Probability_from_0_to_1" title="Fat Chance: Probability from 0 to 1">Fat Chance: Probability from 0 to 1</a></i>, with Benedict Gross and Joe Harris (2019)<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li> <li><i>Elements of ∞-Category Theory</i>, with Dominic Verity, <a rel="nofollow" class="external text" href="http://www.math.jhu.edu/~eriehl/elements.pdf">online draft</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFRiehl2011" class="citation journal cs1">Riehl, Emily (2011). <a rel="nofollow" class="external text" href="http://emis.de/journals/NYJM/j/2011/17-10v.pdf">"Algebraic model structures"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/The_New_York_Journal_of_Mathematics" title="The New York Journal of Mathematics">The New York Journal of Mathematics</a></i>. <b>17</b>: 173–231. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2781914">2781914</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Journal+of+Mathematics&rft.atitle=Algebraic+model+structures&rft.volume=17&rft.pages=173-231&rft.date=2011&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D2781914%23id-name%3DMR&rft.aulast=Riehl&rft.aufirst=Emily&rft_id=http%3A%2F%2Femis.de%2Fjournals%2FNYJM%2Fj%2F2011%2F17-10v.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></span> </li> <li id="cite_note-phdplus-2"><span class="mw-cite-backlink">^ <a 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United States Australian Football League.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Freedom+Captains+Ready+for+IC+Challenge&rft.pub=United+States+Australian+Football+League&rft.date=2017-07-31&rft.aulast=Barrish&rft.aufirst=Brian&rft_id=https%3A%2F%2Fusafl.com%2Fnews%2F20170731%2Ffreedom-captains-ready-ic-challenge&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.highclouds.org/interview-lgbt-movement-and-feminism-with-queer-band-unstraight/">"Interview: LGBT movement and feminism with queer band Unstraight"</a>. <i>Highclouds</i>. 2017-02-15<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-03-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Highclouds&rft.atitle=Interview%3A+LGBT+movement+and+feminism+with+queer+band+Unstraight&rft.date=2017-02-15&rft_id=http%3A%2F%2Fwww.highclouds.org%2Finterview-lgbt-movement-and-feminism-with-queer-band-unstraight%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRiehlVerity2018" class="citation journal cs1">Riehl, Emily; Verity, Dominic (2018). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200828211141/http://journals.mq.edu.au/index.php/higher_structures/article/view/39">"The comprehension construction"</a>. <i>Higher Structures</i>. <b>2</b> (1): 116–190. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1706.10023">1706.10023</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017arXiv170610023R">2017arXiv170610023R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.21136%2FHS.2018.05">10.21136/HS.2018.05</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=3917428">3917428</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51758720">51758720</a>. Archived from <a rel="nofollow" class="external text" href="https://journals.mq.edu.au/index.php/higher_structures/article/view/39">the original</a> on 2020-08-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-06-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Higher+Structures&rft.atitle=The+comprehension+construction&rft.volume=2&rft.issue=1&rft.pages=116-190&rft.date=2018&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51758720%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017arXiv170610023R&rft_id=info%3Aarxiv%2F1706.10023&rft_id=info%3Adoi%2F10.21136%2FHS.2018.05&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D3917428%23id-name%3DMR&rft.aulast=Riehl&rft.aufirst=Emily&rft.au=Verity%2C+Dominic&rft_id=https%3A%2F%2Fjournals.mq.edu.au%2Findex.php%2Fhigher_structures%2Farticle%2Fview%2F39&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRiehl2014" class="citation book cs1">Riehl, Emily (2014). <a rel="nofollow" class="external text" href="http://www.math.jhu.edu/~eriehl/cathtpy"><i>Categorical Homotopy Theory</i></a>. New Mathematical Monographs. Vol. 24. Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-04845-4" title="Special:BookSources/978-1-107-04845-4"><bdi>978-1-107-04845-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/891831279">891831279</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Categorical+Homotopy+Theory&rft.place=Cambridge&rft.series=New+Mathematical+Monographs&rft.pub=Cambridge+University+Press&rft.date=2014&rft_id=info%3Aoclcnum%2F891831279&rft.isbn=978-1-107-04845-4&rft.aulast=Riehl&rft.aufirst=Emily&rft_id=http%3A%2F%2Fwww.math.jhu.edu%2F~eriehl%2Fcathtpy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span> (book website with downloadable pdf). Reviews: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScherer" class="citation journal cs1">Scherer, Jérôme. <i><a href="/wiki/ZbMATH" class="mw-redirect" title="ZbMATH">zbMATH</a></i>. <a href="/wiki/Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:1317.18001">1317.18001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=zbMATH&rft_id=https%3A%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A1317.18001%23id-name%3DZbl&rft.aulast=Scherer&rft.aufirst=J%C3%A9r%C3%B4me&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: untitled periodical (<a href="/wiki/Category:CS1_maint:_untitled_periodical" title="Category:CS1 maint: untitled periodical">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlanc" class="citation journal cs1">Blanc, David A. <i><a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">Mathematical Reviews</a></i>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=3221774">3221774</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Reviews&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D3221774%23id-name%3DMR&rft.aulast=Blanc&rft.aufirst=David+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: untitled periodical (<a href="/wiki/Category:CS1_maint:_untitled_periodical" title="Category:CS1 maint: untitled periodical">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeiss2014" class="citation journal cs1">Weiss, Ittay (July 2014). <a rel="nofollow" class="external text" href="https://www.maa.org/press/maa-reviews/categorical-homotopy-theory">"Review"</a>. <i>MAA Reviews</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=MAA+Reviews&rft.atitle=Review&rft.date=2014-07&rft.aulast=Weiss&rft.aufirst=Ittay&rft_id=https%3A%2F%2Fwww.maa.org%2Fpress%2Fmaa-reviews%2Fcategorical-homotopy-theory&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRiehl2016" class="citation book cs1">Riehl, Emily (2016). <a rel="nofollow" class="external text" href="http://www.math.jhu.edu/~eriehl/context"><i>Category Theory in Context</i></a>. Courier Dover Publications. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-80903-8" title="Special:BookSources/978-0-486-80903-8"><bdi>978-0-486-80903-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1006743127">1006743127</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Category+Theory+in+Context&rft.pub=Courier+Dover+Publications&rft.date=2016&rft_id=info%3Aoclcnum%2F1006743127&rft.isbn=978-0-486-80903-8&rft.aulast=Riehl&rft.aufirst=Emily&rft_id=http%3A%2F%2Fwww.math.jhu.edu%2F~eriehl%2Fcontext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span> (book website with downloadable pdf). Review: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeiss2018" class="citation journal cs1">Weiss, Ittay (April 2018). <a rel="nofollow" class="external text" href="https://www.maa.org/press/maa-reviews/category-theory-in-context">"Review"</a>. <i>MAA Reviews</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=MAA+Reviews&rft.atitle=Review&rft.date=2018-04&rft.aulast=Weiss&rft.aufirst=Ittay&rft_id=https%3A%2F%2Fwww.maa.org%2Fpress%2Fmaa-reviews%2Fcategory-theory-in-context&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrossHarrisRiehl2019" class="citation book cs1"><a href="/wiki/Benedict_Gross" title="Benedict Gross">Gross, Benedict</a>; <a href="/wiki/Joe_Harris_(mathematician)" title="Joe Harris (mathematician)">Harris, Joe</a>; Riehl, Emily (2019). <i>Fat Chance: Probability from 0 to 1</i>. Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fat+Chance%3A+Probability+from+0+to+1&rft.pub=Cambridge+University+Press&rft.date=2019&rft.aulast=Gross&rft.aufirst=Benedict&rft.au=Harris%2C+Joe&rft.au=Riehl%2C+Emily&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span> Reviews: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBollman" class="citation journal cs1">Bollman, Mark. <i>Mathematical Reviews</i>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=3931738">3931738</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Reviews&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D3931738%23id-name%3DMR&rft.aulast=Bollman&rft.aufirst=Mark&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: untitled periodical (<a href="/wiki/Category:CS1_maint:_untitled_periodical" title="Category:CS1 maint: untitled periodical">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaditz" class="citation journal cs1">Paditz, Ludwig. <i>zbMATH</i>. <a href="/wiki/Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:1423.00005">1423.00005</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=zbMATH&rft_id=https%3A%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A1423.00005%23id-name%3DZbl&rft.aulast=Paditz&rft.aufirst=Ludwig&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: untitled periodical (<a href="/wiki/Category:CS1_maint:_untitled_periodical" title="Category:CS1 maint: untitled periodical">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNespolo2019" class="citation journal cs1">Nespolo, Massimo (November 2019). <i>Journal of Applied Crystallography</i>. <b>52</b> (6): 1467–1468. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1107%2Fs1600576719014055">10.1107/s1600576719014055</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Crystallography&rft.volume=52&rft.issue=6&rft.pages=1467-1468&rft.date=2019-11&rft_id=info%3Adoi%2F10.1107%2Fs1600576719014055&rft.aulast=Nespolo&rft.aufirst=Massimo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: untitled periodical (<a href="/wiki/Category:CS1_maint:_untitled_periodical" title="Category:CS1 maint: untitled periodical">link</a>)</span></li></ul> </span></li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Emily_Riehl&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://emilyriehl.github.io/">"Emily Riehl's homepage"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Emily+Riehl%27s+homepage&rft_id=https%3A%2F%2Femilyriehl.github.io%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEmily+Riehl" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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