CINXE.COM

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en-ca"> <head> <title>nForum - model structure on dg-algebras</title> <link rel="shortcut icon" href="/themes/nforum/styles/nforum/favicon.ico" /> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <link rel="stylesheet" type="text/css" href="/extensions/TagThis/theme/tagthis.css" /> <link rel="stylesheet" type="text/css" href="/themes/nforum/styles/nforum/vanilla.css" media="screen" /> <link rel="stylesheet" type="text/css" href="/themes/nforum/styles/nforum/vanilla.print.css" media="print" /> <link rel="stylesheet" type="text/css" href="/extensions/GuestPost/style.css" /> <link rel="stylesheet" type="text/css" href="/extensions/GuestSignIn/style.css" /> <link rel="stylesheet" type="text/css" href="/extensions/OpenID/css/openid.css" /> <link rel="stylesheet" type="text/css" href="/extensions/PreviewPost/preview.css" /> <script type="text/javascript" src="/js/global.js"></script> <script type="text/javascript" src="/js/vanilla.js"></script> <script type="text/javascript" src="/js/ajax.js"></script> <script type="text/javascript" src="/js/ac.js"></script> <script type="text/javascript" src="/extensions/JQuery/jquery-1.4.2.min.js"></script> <script type="text/javascript" src="/extensions/OpenID/js/openid-jquery.js"></script> <script type="text/javascript" src="/extensions/OpenID/js/openid-en.js"></script> <script type="text/javascript" src="/extensions/MarkdownItex/itex.js"></script> <script type="text/javascript" src="/extensions/MembersList/library/tablesort.js"></script> <script type="text/javascript" src="/extensions/MembersList/library/paginate.js"></script> <script type="text/javascript" src="/extensions/PreviewPost/preview.js"></script> <script type="text/javascript" src="/extensions/CustomStyles/functions.js"></script> <script type="text/javascript" src="/js/prototype.js"></script> <script type="text/javascript" src="/js/scriptaculous.js"></script> <script type="text/javascript" src="/extensions/Notify/functions.js"></script> <link rel="alternate" type="application/rss+xml" href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Comments&Page=1&Feed=RSS2&DiscussionID=356&FeedTitle=Discussion+Feed+%28model+structure+on+dg-algebras%29" title="Discussion Feed (RSS2)" /> <link rel="alternate" type="application/atom+xml" href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Comments&Page=1&Feed=ATOM&DiscussionID=356&FeedTitle=Discussion+Feed+%28model+structure+on+dg-algebras%29" title="Discussion Feed (ATOM)" /> <script type="text/javascript"> ( function($) { $(document).ready(function() { openid.init('openid_identifier',true); openid.setFormID('frmSignInOpenID'); }); }) (jQuery ); </script><script type="text/x-mathjax-config">MathJax.Hub.Config({TeX: {extensions: ["AMScd.js"]}});</script><script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=MML_HTMLorMML-full"></script></head> <body id="CommentsPage" > <div id="SiteContainer"><div id="Session">Not signed in (<a href="/people.php?ReturnUrl=http%3A%2F%2Fnforum.ncatlab.org%2Fdiscussion%2F356%2F">Sign In</a>)</div><div id="Header"> <a id="pgtop"></a> <span id="logo"></span> <h1> nForum </h1> <div id="TagLine">A discussion forum about contributions to the <a href="https://ncatlab.org/">nLab wiki</a> and related areas of mathematics, physics, and philosophy.</div><ul><li><a href="/extension.php?PostBackAction=HomeCat" >Home</a></li><li class="TabOn"><a href="/" >Discussions</a></li><li><a href="/categories.php" >Categories</a></li><li><a href="/search.php" >Search</a></li><li><a href="https://ncatlab.org/nlab/show/HomePage" >nLab</a></li><li><a href="https://ncatlab.org/nlabmeta/show/Welcome+to+the+nForum" >Help</a></li></ul> </div><div id="Body"><div id="Panel"><ul> <li> <h2>Discussion Feed</h2> <ul><li> <a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Comments&Page=1&Feed=RSS2&DiscussionID=356&FeedTitle=Discussion+Feed+%28model+structure+on+dg-algebras%29" title="Subscribe to this feed..." class="RSS2">RSS2</a></li><li> <a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Comments&Page=1&Feed=ATOM&DiscussionID=356&FeedTitle=Discussion+Feed+%28model+structure+on+dg-algebras%29" title="Subscribe to this feed..." class="ATOM">ATOM</a></li></ul> </li> </ul><div id="GuestSignIn"> <h2>Not signed in</h2> <p>Want to take part in these discussions? Sign in if you have an account, or apply for one below</p> <fieldset><form id="frmSignInUser" method="post" action="https://nforum.ncatlab.org/people/"> <div> <input name="PostBackAction" value="SignIn" type="hidden" /> <input name="ReturnUrl" value="http://nforum.ncatlab.org/discussion/356/" type="hidden" /> <ul> <li><label for="txtUsername">Username</label> <input id="txtUsername" name="Username" value="" class="Input" maxlength="20" type="text" /> </li> <li><label for="txtPassword">Password</label> <input id="txtPassword" name="Password" value="" class="Input" type="password" /> </li> <li id="RememberMe"><label for="RememberMeID"> <input name="RememberMe" value="1" id="RememberMeID" type="checkbox" checked="checked" /> Remember me</label> </li> <li> <input name="userSignIn" value="Sign In" class="Button" type="submit" /> </li> </ul> </div> </form> </fieldset> <fieldset><form id="frmSignInOpenID" method="post" action="https://nforum.ncatlab.org/people/"> <input name="PostBackAction" value="SignIn" type="hidden" /> <div> <ul> <li>Sign in using OpenID <div id="openid_choice"> <div id="openid_btns"></div> </div> <div id="openid_input_area"> <input id="openid_identifier" name="openid_identifier" type="text" value="http://" /> </div> </li> <li id="RememberMe"><label for="RememberMeID"> <input name="RememberMe" value="1" id="RememberMeID" type="checkbox" checked="checked" /> Remember me</label> </li> <li><input name="openidSignIn" value="Sign In" class="Button" type="submit" /></li> </ul> </div></form></fieldset> <ul class="MembershipOptionLinks"> <li class="ForgotPasswordLink"><a href="https://nforum.ncatlab.org/people/?PostBackAction=PasswordRequestForm">Forgot your password?</a></li> <li class="ApplyForMembershipLink"><a href="https://nforum.ncatlab.org/people/?PostBackAction=ApplyForm">Apply for membership</a></li> </ul></div><h2>Site Tag Cloud</h2><div id="TagCloud"><span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=2-category" class="TagLink">2-category</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=2-category-theory" class="TagLink">2-category-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=abelian-categories" class="TagLink">abelian-categories</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=adjoint" class="TagLink">adjoint</a></span> <span style="font-size:162%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=algebra" class="TagLink">algebra</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=algebraic" class="TagLink">algebraic</a></span> <span style="font-size:70%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=algebraic-geometry" class="TagLink">algebraic-geometry</a></span> <span style="font-size:60%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=algebraic-topology" class="TagLink">algebraic-topology</a></span> <span style="font-size:77%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=analysis" class="TagLink">analysis</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=analytic-geometry" class="TagLink">analytic-geometry</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=arithmetic" class="TagLink">arithmetic</a></span> <span style="font-size:71%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=arithmetic-geometry" class="TagLink">arithmetic-geometry</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=book" class="TagLink">book</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=bundles" class="TagLink">bundles</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=calculus" class="TagLink">calculus</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=categorical" class="TagLink">categorical</a></span> <span style="font-size:62%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=categories" class="TagLink">categories</a></span> <span style="font-size:85%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=category" class="TagLink">category</a></span> <span style="font-size:181%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=category-theory" class="TagLink">category-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=chern-weil-theory" class="TagLink">chern-weil-theory</a></span> <span style="font-size:80%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=cohesion" class="TagLink">cohesion</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=cohesive-homotopy-type-theory" class="TagLink">cohesive-homotopy-type-theory</a></span> <span style="font-size:185%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=cohomology" class="TagLink">cohomology</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=colimits" class="TagLink">colimits</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=combinatorics" class="TagLink">combinatorics</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=complex" class="TagLink">complex</a></span> <span style="font-size:83%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=complex-geometry" class="TagLink">complex-geometry</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=computable-mathematics" class="TagLink">computable-mathematics</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=computer-science" class="TagLink">computer-science</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=constructive" class="TagLink">constructive</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=cosmology" class="TagLink">cosmology</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=definitions" class="TagLink">definitions</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=deformation-theory" class="TagLink">deformation-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=descent" class="TagLink">descent</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=diagrams" class="TagLink">diagrams</a></span> <span style="font-size:60%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=differential" class="TagLink">differential</a></span> <span style="font-size:71%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=differential-cohomology" class="TagLink">differential-cohomology</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=differential-equations" class="TagLink">differential-equations</a></span> <span style="font-size:138%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=differential-geometry" class="TagLink">differential-geometry</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=digraphs" class="TagLink">digraphs</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=duality" class="TagLink">duality</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=elliptic-cohomology" class="TagLink">elliptic-cohomology</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=enriched" class="TagLink">enriched</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=fibration" class="TagLink">fibration</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=foundation" class="TagLink">foundation</a></span> <span style="font-size:82%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=foundations" class="TagLink">foundations</a></span> <span style="font-size:76%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=functional-analysis" class="TagLink">functional-analysis</a></span> <span style="font-size:59%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=functor" class="TagLink">functor</a></span> <span style="font-size:60%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=gauge-theory" class="TagLink">gauge-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=gebra" class="TagLink">gebra</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=geometric-quantization" class="TagLink">geometric-quantization</a></span> <span style="font-size:176%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=geometry" class="TagLink">geometry</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=graph" class="TagLink">graph</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=graphs" class="TagLink">graphs</a></span> <span style="font-size:72%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=gravity" class="TagLink">gravity</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=grothendieck" class="TagLink">grothendieck</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=group" class="TagLink">group</a></span> <span style="font-size:101%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=group-theory" class="TagLink">group-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=harmonic-analysis" class="TagLink">harmonic-analysis</a></span> <span style="font-size:59%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher" class="TagLink">higher</a></span> <span style="font-size:126%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-algebra" class="TagLink">higher-algebra</a></span> <span style="font-size:119%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-category-theory" class="TagLink">higher-category-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-differential-geometry" class="TagLink">higher-differential-geometry</a></span> <span style="font-size:123%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-geometry" class="TagLink">higher-geometry</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-lie-theory" class="TagLink">higher-lie-theory</a></span> <span style="font-size:82%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=higher-topos-theory" class="TagLink">higher-topos-theory</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=homological" class="TagLink">homological</a></span> <span style="font-size:87%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=homological-algebra" class="TagLink">homological-algebra</a></span> <span style="font-size:62%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=homotopy" class="TagLink">homotopy</a></span> <span style="font-size:170%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=homotopy-theory" class="TagLink">homotopy-theory</a></span> <span style="font-size:77%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=homotopy-type-theory" class="TagLink">homotopy-type-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=index-theory" class="TagLink">index-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=integration" class="TagLink">integration</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=integration-theory" class="TagLink">integration-theory</a></span> <span style="font-size:57%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=k-theory" class="TagLink">k-theory</a></span> <span style="font-size:90%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=lie-theory" class="TagLink">lie-theory</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=limits" class="TagLink">limits</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=linear" class="TagLink">linear</a></span> <span style="font-size:65%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=linear-algebra" class="TagLink">linear-algebra</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=locale" class="TagLink">locale</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=localization" class="TagLink">localization</a></span> <span style="font-size:102%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=logic" class="TagLink">logic</a></span> <span style="font-size:59%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=mathematics" class="TagLink">mathematics</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=measure-theory" class="TagLink">measure-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=modal" class="TagLink">modal</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=modal-logic" class="TagLink">modal-logic</a></span> <span style="font-size:60%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=model" class="TagLink">model</a></span> <span style="font-size:68%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=model-category-theory" class="TagLink">model-category-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=monad" class="TagLink">monad</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=monads" class="TagLink">monads</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=monoidal" class="TagLink">monoidal</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=monoidal-category-theory" class="TagLink">monoidal-category-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=morphism" class="TagLink">morphism</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=motives" class="TagLink">motives</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=motivic-cohomology" class="TagLink">motivic-cohomology</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=nlab" class="TagLink">nlab</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=nonassociative" class="TagLink">nonassociative</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=noncommutative" class="TagLink">noncommutative</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=noncommutative-geometry" class="TagLink">noncommutative-geometry</a></span> <span style="font-size:61%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=number-theory" class="TagLink">number-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=of" class="TagLink">of</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=operads" class="TagLink">operads</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=operator" class="TagLink">operator</a></span> <span style="font-size:67%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=operator-algebra" class="TagLink">operator-algebra</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=order-theory" class="TagLink">order-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=pages" class="TagLink">pages</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=pasting" class="TagLink">pasting</a></span> <span style="font-size:70%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=philosophy" class="TagLink">philosophy</a></span> <span style="font-size:200%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=physics" class="TagLink">physics</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=pro-object" class="TagLink">pro-object</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=probability" class="TagLink">probability</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=probability-theory" class="TagLink">probability-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantization" class="TagLink">quantization</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum" class="TagLink">quantum</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum-field" class="TagLink">quantum-field</a></span> <span style="font-size:162%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum-field-theory" class="TagLink">quantum-field-theory</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum-mechanics" class="TagLink">quantum-mechanics</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum-physics" class="TagLink">quantum-physics</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=quantum-theory" class="TagLink">quantum-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=question" class="TagLink">question</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=representation" class="TagLink">representation</a></span> <span style="font-size:86%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=representation-theory" class="TagLink">representation-theory</a></span> <span style="font-size:66%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=riemannian-geometry" class="TagLink">riemannian-geometry</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=scheme" class="TagLink">scheme</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=schemes" class="TagLink">schemes</a></span> <span style="font-size:59%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=set" class="TagLink">set</a></span> <span style="font-size:62%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=set-theory" class="TagLink">set-theory</a></span> <span style="font-size:55%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=sheaf" class="TagLink">sheaf</a></span> <span style="font-size:59%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=simplicial" class="TagLink">simplicial</a></span> <span style="font-size:56%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=space" class="TagLink">space</a></span> <span style="font-size:61%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=spin-geometry" class="TagLink">spin-geometry</a></span> <span style="font-size:122%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=stable-homotopy-theory" class="TagLink">stable-homotopy-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=stack" class="TagLink">stack</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=string" class="TagLink">string</a></span> <span style="font-size:104%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=string-theory" class="TagLink">string-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=superalgebra" class="TagLink">superalgebra</a></span> <span style="font-size:76%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=supergeometry" class="TagLink">supergeometry</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=svg" class="TagLink">svg</a></span> <span style="font-size:76%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=symplectic-geometry" class="TagLink">symplectic-geometry</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=synthetic-differential-geometry" class="TagLink">synthetic-differential-geometry</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=terminology" class="TagLink">terminology</a></span> <span style="font-size:101%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=theory" class="TagLink">theory</a></span> <span style="font-size:137%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=topology" class="TagLink">topology</a></span> <span style="font-size:71%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=topos" class="TagLink">topos</a></span> <span style="font-size:89%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=topos-theory" class="TagLink">topos-theory</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=tqft" class="TagLink">tqft</a></span> <span style="font-size:58%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=type" class="TagLink">type</a></span> <span style="font-size:118%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=type-theory" class="TagLink">type-theory</a></span> <span style="font-size:54%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=universal" class="TagLink">universal</a></span> <span style="font-size:53%"><a href="https://nforum.ncatlab.org/search/?PostBackAction=Search&Type=Topics&Tag=variational-calculus" class="TagLink">variational-calculus</a></span></div><p id="AboutVanilla"><a href="http://getvanilla.com">Vanilla 1.1.10</a> is a product of <a href="http://lussumo.com">Lussumo</a>. More Information: <a href="http://lussumo.com/docs">Documentation</a>, <a href="http://lussumo.com/community">Community Support</a>.</p></div> <div id="Content"><div id="NoticeCollector" class="Notices"><div class="Notice"><strong>Welcome to nForum</strong> <br />If you want to take part in these discussions either <a href="/people.php?ReturnUrl=http%3A%2F%2Fnforum.ncatlab.org%2Fdiscussion%2F356%2F">sign in now</a> (if you have an account), <a href="https://nforum.ncatlab.org/people/?PostBackAction=ApplyForm">apply for one now</a> (if you don't).</div></div><div class="ContentInfo Top"> <h1><a href="https://nforum.ncatlab.org/5/"><a href="https://nforum.ncatlab.org/18/">nLab</a> > </a> <a href="https://nforum.ncatlab.org/5/">Latest Changes</a>: model structure on dg-algebras</h1> <a href="#pgbottom">Bottom of Page</a> <div class="PageInfo"> <p>1 to 21 of 21</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div> <div id="ContentBody"> <script type="text/javascript"> //<![CDATA[ function toggle_source(id) { var mysrc = document.getElementById("CommentBody_" + id).firstChild; if (mysrc.className == "source") { if (mysrc.style.display == "none") { mysrc.style.display = "block"; } else { mysrc.style.display = "none"; } } } var commentIds = new Array(0); function hide_sources() { for (i = 0; i < commentIds.length; i++) { var myself = document.getElementById("Source" + commentIds[i]); var mycmt = document.getElementById("CommentBody_" + commentIds[i]); if (mycmt.firstChild.className != "source") { myself.style.display = "none"; } } } window.onload = hide_sources; //]]> </script> <ol id="Comments"><li id="Comment_2304"> <a id="Item_1"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>1.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 11th 2009</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2304#Comment_2304">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2304"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>Fixed the comments in the reference list at [[model structure on dg-algebras]]: Gelfand-Manin just discuss the commutative case. The noncommutative case seems to be due to the Jardine reference. Or does anyone know an earlier one?</code></div><div> <p>Fixed the comments in the reference list at <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">model structure on dg-algebras</a>: Gelfand-Manin just discuss the commutative case. The noncommutative case seems to be due to the Jardine reference. Or does anyone know an earlier one?</p> </div> </div> </li><li id="Comment_2312" class="Alternate"> <a id="Item_2"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>2.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 11th 2009</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2312#Comment_2312">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2312"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>I have a question at [[model structure on dg-algebras]] on the invariant characterization of commutative dg-algebras within all dg-algebras.</code></div><div> <p>I have a question at <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">model structure on dg-algebras</a> on the invariant characterization of commutative dg-algebras within all dg-algebras.</p> </div> </div> </li><li id="Comment_2322"> <a id="Item_3"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>3.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 11th 2009</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2322#Comment_2322">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2322"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>I added an "Idea" section to [[model structure on dg-algebras]]</code></div><div> <p>I added an "Idea" section to <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">model structure on dg-algebras</a></p> </div> </div> </li><li id="Comment_2334" class="Alternate"> <a id="Item_4"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>4.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 11th 2009</li><li><em>(edited Nov 11th 2009)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2334#Comment_2334">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2334"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>I added a theorem from the book by Igor Kriz and Peter May about how commutative dg-algebras already exhaust, up to weak equivalence, all homotopy-cmmutative dg-algebras to [[model structure on dg-algebra]]s. (this might better fit into some other entry eventually, though)</code></div><div> <p>I added a theorem from the book by Igor Kriz and Peter May about how commutative dg-algebras already exhaust, up to weak equivalence, all homotopy-cmmutative dg-algebras to <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebra">model structure on dg-algebra</a>s.</p> <p>(this might better fit into some other entry eventually, though)</p> </div> </div> </li><li id="Comment_2352"> <a id="Item_5"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>5.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 11th 2009</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2352#Comment_2352">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2352"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>Added the statement that the forgetful functor from commutative dg-algebras to all dg-algebras is the right adjoint part of a Quillen adjunction with respect to the given modelstructures.</code></div><div> <p>Added the statement that the forgetful functor from commutative dg-algebras to all dg-algebras is the right adjoint part of a Quillen adjunction with respect to the given modelstructures.</p> </div> </div> </li><li id="Comment_2355" class="Alternate"> <a id="Item_6"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>6.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/10/">zskoda</a></li> <li><span>CommentTime</span>Nov 11th 2009</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2355#Comment_2355">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2355"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/10/">zskoda</a></span><br/><span class="sourceType">Format: Text</span><code>I would look into Hinich's 1995 or so paper, for a possible earlier reference.</code></div><div> I would look into Hinich's 1995 or so paper, for a possible earlier reference. </div> </div> </li><li id="Comment_2375"> <a id="Item_7"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>7.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 12th 2009</li><li><em>(edited Nov 12th 2009)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=2375#Comment_2375">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_2375"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: Markdown</span><code>created a section on <a href="http://ncatlab.org/nlab/show/model+structure+on+dg-algebras#cofibrations_sullivan_algebras_8">cofibrations in CdgAlg</a> and hence on Sullivan algebras. Created entry for [[Dennis Sullivan]] in that context. Always nice to create an entry and see that the "timeline"-entry was already requesting it. I suppose I'll have the following sorted out in a minute, but maybe somebody is quicker with helping me: in the definition of a relative Suillvan algebra <latex> (A,d) \hookrightarrow (A \otimes \wedge V, d') </latex> I suppose we do require that <latex> d' </latex> restricted to <latex> A</latex> acts like <latex> d </latex> plus a term that contains elements in V ?</code></div><div> <p>created a section on <a href="http://ncatlab.org/nlab/show/model+structure+on+dg-algebras#cofibrations_sullivan_algebras_8">cofibrations in CdgAlg</a> and hence on Sullivan algebras.</p> <p>Created entry for <a href="https://ncatlab.org/nlab/show/Dennis+Sullivan">Dennis Sullivan</a> in that context. Always nice to create an entry and see that the "timeline"-entry was already requesting it.</p> <p>I suppose I'll have the following sorted out in a minute, but maybe somebody is quicker with helping me:</p> <p>in the definition of a relative Suillvan algebra <img src="/extensions/vLaTeX/cache/latex_4e71b6aa140c2bf54207912d68286c3b.png" title=" (A,d) \hookrightarrow (A \otimes \wedge V, d') " style="vertical-align: -20%;" class="tex" alt=" (A,d) \hookrightarrow (A \otimes \wedge V, d') "/> I suppose we do require that <img src="/extensions/vLaTeX/cache/latex_21e4d200c3cd4322cc69743b247bb425.png" title=" d' " style="vertical-align: -20%;" class="tex" alt=" d' "/> restricted to <img src="/extensions/vLaTeX/cache/latex_c7845c65e7c03bcf8156e1be56e70492.png" title=" A" style="vertical-align: -20%;" class="tex" alt=" A"/> acts like <img src="/extensions/vLaTeX/cache/latex_3ff14cb72c5868b1d32aabf73154ef69.png" title=" d " style="vertical-align: -20%;" class="tex" alt=" d "/> plus a term that contains elements in V ?</p> </div> </div> </li><li id="Comment_18827" class="Alternate"> <a id="Item_8"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>8.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Nov 29th 2010</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=18827#Comment_18827">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_18827"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I started at [[model structure on dg-algebras]] a new subsection on <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#Unbounded">Unbounded dg-algebras</a>, stating a basic existence result.</code></div><div> <p>I started at <a href="https://ncatlab.org/nlab/show/model structure on dg-algebras">model structure on dg-algebras</a> a new subsection on <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#Unbounded">Unbounded dg-algebras</a>, stating a basic existence result.</p> </div> </div> </li><li id="Comment_19283"> <a id="Item_9"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>9.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Dec 9th 2010</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=19283#Comment_19283">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_19283"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added a section <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#SimplicialHomObjects">Simplicial hom-objects</a> to [[model structure on dg-algebras]] on the derived hom-spaces for unbounded commutative dg-algebras (over a field of char 0).</code></div><div> <p>added a section <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#SimplicialHomObjects">Simplicial hom-objects</a> to <a href="https://ncatlab.org/nlab/show/model structure on dg-algebras">model structure on dg-algebras</a> on the derived hom-spaces for unbounded commutative dg-algebras (over a field of char 0).</p> </div> </div> </li><li id="Comment_19285" class="Alternate"> <a id="Item_10"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>10.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Dec 9th 2010</li><li><em>(edited Dec 9th 2010)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=19285#Comment_19285">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_19285"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>okay, I think I finally have assembled the full proof that the derived copowering of undbounded commutative dg-algebras (over field of char 0) over degreewise finite simplicial sets is given by the polynomial-differential-forms-on-simplices-functors. I have written this out now at <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#DerivedPowering">Derived powering over sSet</a>. This provides the missing detail for the discussion that $\mathcal{O}(S^1) \simeq k \oplus k[-1]$ over at [[Hochschild cohomology]]. This is supposed to be all very obvious, but it took me a bit to assemble all the details properly, anyway. I now moved other discussion of the model structure on commutative unbounded dg-algebras from the Hochschild entry over to [[model structure on dg-algebras]]. This mainly constituting the other new section <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#DerivedCopowering">Derived co-powering over sSet</a>.</code></div><div> <p>okay, I think I finally have assembled the full proof that the derived copowering of undbounded commutative dg-algebras (over field of char 0) over degreewise finite simplicial sets is given by the polynomial-differential-forms-on-simplices-functors. I have written this out now at <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#DerivedPowering">Derived powering over sSet</a>.</p> <p>This provides the missing detail for the discussion that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>&Oscr;</mi><mo stretchy="false">(</mo><msup><mi>S</mi> <mn>1</mn></msup><mo stretchy="false">)</mo><mo>&simeq;</mo><mi>k</mi><mo>&oplus;</mo><mi>k</mi><mo stretchy="false">[</mo><mo lspace="0.11111em" rspace="0em">−</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\mathcal{O}(S^1) \simeq k \oplus k[-1]</annotation></semantics></math> over at <a href="https://ncatlab.org/nlab/show/Hochschild cohomology">Hochschild cohomology</a>. This is supposed to be all very obvious, but it took me a bit to assemble all the details properly, anyway.</p> <p>I now moved other discussion of the model structure on commutative unbounded dg-algebras from the Hochschild entry over to <a href="https://ncatlab.org/nlab/show/model structure on dg-algebras">model structure on dg-algebras</a>. This mainly constituting the other new section <a href="http://nlab.mathforge.org/nlab/show/model+structure+on+dg-algebras#DerivedCopowering">Derived co-powering over sSet</a>.</p> </div> </div> </li><li id="Comment_19301"> <a id="Item_11"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>11.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Dec 10th 2010</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=19301#Comment_19301">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_19301"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I added statement and proof that $([n] \mapsto Hom(A, B \otimes \Omega^\bullet_{poly}(\Delta[n])))$ is a Kan complex when $A$ is cofibrant. Also added an earlier reference by Ginot et al where it is discussed that their "derived copowering" of cdgAlg over sSet indeed lands in _commutative_ dg-algebras. I'll try to add more technical details on how this works later on.</code></div><div> <p>I added statement and proof that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo><mo>&map;</mo><mi>Hom</mi><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>&otimes;</mo><msubsup><mi>Ω</mi> <mi>poly</mi> <mo>&bullet;</mo></msubsup><mo stretchy="false">(</mo><mi>Δ</mi><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">([n] \mapsto Hom(A, B \otimes \Omega^\bullet_{poly}(\Delta[n])))</annotation></semantics></math> is a Kan complex when <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math> is cofibrant.</p> <p>Also added an earlier reference by Ginot et al where it is discussed that their “derived copowering” of cdgAlg over sSet indeed lands in <em>commutative</em> dg-algebras. I’ll try to add more technical details on how this works later on.</p> </div> </div> </li><li id="Comment_48427" class="Alternate"> <a id="Item_12"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>12.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jul 16th 2014</li><li><em>(edited Jul 16th 2014)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=48427#Comment_48427">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_48427"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>there was an [old question](http://mathoverflow.net/q/5031/381) of how (to which extent) the homotopy theory of commutative dg-algebras is homotopy-faithful inside that of all dg-algebras. Recently there appeared some discussion of this issue in * [[Ilias Amrani]], _Comparing commutative and associative unbounded differential graded algebras over Q from homotopical point of view_ ([arXiv:1401.7285](http://arxiv.org/abs/1401.7285)) * [[Ilias Amrani]], _Rational homotopy theory of function spaces and Hochschild cohomology_ ([arXiv:1406.6269](http://arxiv.org/abs/1406.6269)) I have added pointers to this [here](http://www.ncatlab.org/nlab/show/model+structure+on+dg-algebras#CommVsNoncomm).</code></div><div> <p>there was an <a href="http://mathoverflow.net/q/5031/381">old question</a> of how (to which extent) the homotopy theory of commutative dg-algebras is homotopy-faithful inside that of all dg-algebras.</p> <p>Recently there appeared some discussion of this issue in</p> <ul> <li><p><a href="https://ncatlab.org/nlab/show/Ilias Amrani">Ilias Amrani</a>, <em>Comparing commutative and associative unbounded differential graded algebras over Q from homotopical point of view</em> (<a href="http://arxiv.org/abs/1401.7285">arXiv:1401.7285</a>)</p></li> <li><p><a href="https://ncatlab.org/nlab/show/Ilias Amrani">Ilias Amrani</a>, <em>Rational homotopy theory of function spaces and Hochschild cohomology</em> (<a href="http://arxiv.org/abs/1406.6269">arXiv:1406.6269</a>)</p></li> </ul> <p>I have added pointers to this <a href="http://www.ncatlab.org/nlab/show/model+structure+on+dg-algebras#CommVsNoncomm">here</a>.</p> </div> </div> </li><li id="Comment_61369"> <a id="Item_13"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>13.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Feb 21st 2017</li><li><em>(edited Feb 21st 2017)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=61369#Comment_61369">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_61369"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I have added to the section on the Bousfield-Gugenheim model structure a subsection on its [simplicial hom-complexes](https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#HomComplexes) which almost but not quite, make for a simplicial model category structure.</code></div><div> <p>I have added to the section on the Bousfield-Gugenheim model structure a subsection on its <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#HomComplexes">simplicial hom-complexes</a> which almost but not quite, make for a simplicial model category structure.</p> </div> </div> </li><li id="Comment_86345" class="Alternate"> <a id="Item_14"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>14.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Aug 19th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=86345#Comment_86345">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86345"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>trying to bring some order into the list of references, adding some subsections... <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/63">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/63">v63</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>trying to bring some order into the list of references, adding some subsections…</p> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/63">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/63">v63</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_86349"> <a id="Item_15"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>15.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Aug 19th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=86349#Comment_86349">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86349"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>have equipped more of the Definitions/Propositions with pointers to page-and-verse in Bousfield-Gugenheim and in Gelfand-Manin. <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/63">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/63">v63</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>have equipped more of the Definitions/Propositions with pointers to page-and-verse in Bousfield-Gugenheim and in Gelfand-Manin.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/63">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/63">v63</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_86370" class="Alternate"> <a id="Item_16"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>16.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Aug 21st 2020</li><li><em>(edited Aug 21st 2020)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=86370#Comment_86370">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86370"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added full publication data to: * [[Paul Goerss]], [[Kirsten Schemmerhorn]], _Model categories and simplicial methods_, Notes from lectures given at the University of Chicago, August 2004, in: _Interactions between Homotopy Theory and Algebra_, Contemporary Mathematics 436, AMS 2007([arXiv:math.AT/0609537](http://arxiv.org/abs/math.AT/0609537), [doi:10.1090/conm/436](http://dx.doi.org/10.1090/conm/436)) Around Example 3.7, these authors make (somewhat implicitly) the observation that the Bousfield-Gugenheim model structure on connective rational dgc-algebras (which B&G and later Gelfand&Manin establish by laborious checks) is simply that right transferred from the projective model structure on chain complexes -- which makes the proof that relative Sullivan models are cofibrations a triviality. So this is all very nice, and highlighted as such in Hess's recview. But neither of these authors states this as a theorem that could be properly cited as such, instead they leave it at side remarks. Is there any author who has published this in more citeable form? <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/67">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/67">v67</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>Added full publication data to:</p> <ul> <li><a href="https://ncatlab.org/nlab/show/Paul Goerss">Paul Goerss</a>, <a href="https://ncatlab.org/nlab/show/Kirsten Schemmerhorn">Kirsten Schemmerhorn</a>, <em>Model categories and simplicial methods</em>, Notes from lectures given at the University of Chicago, August 2004, in: <em>Interactions between Homotopy Theory and Algebra</em>, Contemporary Mathematics 436, AMS 2007(<a href="http://arxiv.org/abs/math.AT/0609537">arXiv:math.AT/0609537</a>, <a href="http://dx.doi.org/10.1090/conm/436">doi:10.1090/conm/436</a>)</li> </ul> <p>Around Example 3.7, these authors make (somewhat implicitly) the observation that the Bousfield-Gugenheim model structure on connective rational dgc-algebras (which B&G and later Gelfand&Manin establish by laborious checks) is simply that right transferred from the projective model structure on chain complexes – which makes the proof that relative Sullivan models are cofibrations a triviality.</p> <p>So this is all very nice, and highlighted as such in Hess’s recview. But neither of these authors states this as a theorem that could be properly cited as such, instead they leave it at side remarks. Is there any author who has published this in more citeable form?</p> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/67">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/67">v67</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_86420"> <a id="Item_17"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>17.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Aug 23rd 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=86420#Comment_86420">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86420"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added paragraph on the [[Quillen adjunction between simplicial sets and connective dgc-algebras]] <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/70">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/70">v70</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>added paragraph on the <a href="https://ncatlab.org/nlab/show/Quillen adjunction between simplicial sets and connective dgc-algebras">Quillen adjunction between simplicial sets and connective dgc-algebras</a></p> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/70">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/70">v70</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_86572" class="Alternate"> <a id="Item_18"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>18.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Sep 1st 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=86572#Comment_86572">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_86572"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added statement ([here](https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#PreservationOfWeakEquivalencesUnderPushout)) that quasi-isos are preserved by pushout along relative Sullivan algebras <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/71">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/71">v71</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>added statement (<a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#PreservationOfWeakEquivalencesUnderPushout">here</a>) that quasi-isos are preserved by pushout along relative Sullivan algebras</p> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/71">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/71">v71</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_93699"> <a id="Item_19"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>19.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jul 7th 2021</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=93699#Comment_93699">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_93699"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I have added ([here](https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#ExtensionOfScalarsQuillenAdjunction)) statement and proof of the change-of-scalars Quillen adjunction $$ \big( dgcAlg^{\geq 0}_k \big)_{proj} \underoverset {\underset{res_{\mathbb{Q}}}{\longrightarrow}} {\overset{ (-) \otimes_{\mathbb{Q}} \mathbb{R} }{\longleftarrow}} {\bot_{\mathrlap{Qu}}} \big( dgcAlg^{\geq 0}_{\mathbb{Q}} \big)_{proj} $$ <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/75">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/75">v75</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></code></div><div> <p>I have added (<a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras#ExtensionOfScalarsQuillenAdjunction">here</a>) statement and proof of the change-of-scalars Quillen adjunction</p> <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mo maxsize="1.2em" minsize="1.2em">(</mo><msubsup><mi>dgcAlg</mi> <mi>k</mi> <mrow><mo>&geq;</mo><mn>0</mn></mrow></msubsup><msub><mo maxsize="1.2em" minsize="1.2em">)</mo> <mi>proj</mi></msub><munderover><mrow><msub><mo>&bot;</mo> <mpadded width="0px"><mi>Qu</mi></mpadded></msub></mrow><munder><mo>&longrightarrow;</mo><mrow><msub><mi>res</mi> <mi>&Qopf;</mi></msub></mrow></munder><mover><mo>&longleftarrow;</mo><mrow><mo stretchy="false">(</mo><mo lspace="0.11111em" rspace="0em">−</mo><mo stretchy="false">)</mo><msub><mo>&otimes;</mo> <mi>&Qopf;</mi></msub><mi>&Ropf;</mi></mrow></mover></munderover><mo maxsize="1.2em" minsize="1.2em">(</mo><msubsup><mi>dgcAlg</mi> <mi>&Qopf;</mi> <mrow><mo>&geq;</mo><mn>0</mn></mrow></msubsup><msub><mo maxsize="1.2em" minsize="1.2em">)</mo> <mi>proj</mi></msub></mrow><annotation encoding="application/x-tex"> \big( dgcAlg^{\geq 0}_k \big)_{proj} \underoverset {\underset{res_{\mathbb{Q}}}{\longrightarrow}} {\overset{ (-) \otimes_{\mathbb{Q}} \mathbb{R} }{\longleftarrow}} {\bot_{\mathrlap{Qu}}} \big( dgcAlg^{\geq 0}_{\mathbb{Q}} \big)_{proj} </annotation></semantics></math> <p><a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+dg-algebras/75">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+dg-algebras/75">v75</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+dg-algebras">current</a></p> </div> </div> </li><li id="Comment_93808" class="Alternate"> <a id="Item_20"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>20.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/24/">Todd_Trimble</a></li> <li><span>CommentTime</span>Jul 11th 2021</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=93808#Comment_93808">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_93808"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/24/">Todd_Trimble</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Changed $\mathbb{R}$ to $k$.</code></div><div> <p>Changed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>&Ropf;</mi></mrow><annotation encoding="application/x-tex">\mathbb{R}</annotation></semantics></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math>.</p> </div> </div> </li><li id="Comment_93809"> <a id="Item_21"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>21.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jul 11th 2021</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/356/model-structure-on-dgalgebras/?Focus=93809#Comment_93809">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_93809"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Ah, right. Thanks.</code></div><div> <p>Ah, right. Thanks.</p> </div> </div> </li></ol> </div><div class="ContentInfo Middle"> <div class="PageInfo"> <p>1 to 21 of 21</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div></div> <a id="pgbottom" > </a> </div> </div></body> </html>