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It does not yet have a dedicated thread; feel free to create one, giving it the same name as the title of this page" style="color:black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <div class="rightHandSide"> <div class="toc clickDown" tabindex="0"> <h3 id="context">Context</h3> <h4 id="model_category_theory">Model category theory</h4> <div class="hide"><div> <a class="existingWikiWord" href="/nlab/show/model+category">model category</a>, <a class="existingWikiWord" href="/nlab/show/model+%28infinity%2C1%29-category">model <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mn>∞</mn> </mrow> <annotation encoding="application/x-tex">\infty</annotation> </semantics> </math>-category</a> Definitions <ul> <li> <a class="existingWikiWord" href="/nlab/show/category+with+weak+equivalences">category with weak equivalences</a> (<a class="existingWikiWord" href="/nlab/show/relative+category">relative category</a>, <a class="existingWikiWord" href="/nlab/show/homotopical+category">homotopical category</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/fibration">fibration</a>, <a class="existingWikiWord" href="/nlab/show/cofibration">cofibration</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/weak+factorization+system">weak factorization system</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/resolution">resolution</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/cell+complex">cell complex</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/small+object+argument">small object argument</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/homotopy+%28as+an+operation%29">homotopy</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/homotopy+category">homotopy category</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thickmathspace"></mspace></mrow><annotation encoding="application/x-tex">\;</annotation></semantics></math><a class="existingWikiWord" href="/nlab/show/homotopy+category+of+a+model+category">of a model category</a> </li> </ul> Morphisms <ul> <li> <a class="existingWikiWord" href="/nlab/show/Quillen+adjunction">Quillen adjunction</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Quillen+equivalence">Quillen equivalence</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Quillen+bifunctor">Quillen bifunctor</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/derived+functor">derived functor</a> </li> </ul> </li> </ul> Universal constructions <ul> <li> <a class="existingWikiWord" href="/nlab/show/homotopy+Kan+extension">homotopy Kan extension</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/homotopy+limit">homotopy limit</a>/<a class="existingWikiWord" href="/nlab/show/homotopy+colimit">homotopy colimit</a> <a class="existingWikiWord" href="/nlab/show/homotopy+weighted+colimit">homotopy weighted (co)limit</a> <a class="existingWikiWord" href="/nlab/show/homotopy+coend">homotopy (co)end</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bousfield-Kan+map">Bousfield-Kan map</a> </li> </ul> Refinements <ul> <li> <a class="existingWikiWord" href="/nlab/show/monoidal+model+category">monoidal model category</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/monoidal+Quillen+adjunction">monoidal Quillen adjunction</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/enriched+model+category">enriched model category</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/enriched+Quillen+adjunction">enriched Quillen adjunction</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/monoidal+enriched+model+category">monoidal enriched model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/simplicial+model+category">simplicial model category</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/simplicial+Quillen+adjunction">simplicial Quillen adjunction</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/simplicial+monoidal+model+category">simplicial monoidal model category</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/cofibrantly+generated+model+category">cofibrantly generated model category</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/combinatorial+model+category">combinatorial model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/cellular+model+category">cellular model category</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/algebraic+model+category">algebraic model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/compactly+generated+model+category">compactly generated model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/proper+model+category">proper model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/cartesian+closed+model+category">cartesian closed model category</a>, <a class="existingWikiWord" href="/nlab/show/locally+cartesian+closed+model+category">locally cartesian closed model category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/stable+model+category">stable model category</a> </li> </ul> Producing new model structures <ul> <li> <a class="existingWikiWord" href="/nlab/show/global+model+structures+on+functor+categories">on functor categories (global)</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Reedy+model+structure">Reedy model structure</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+an+overcategory">on slice categories</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bousfield+localization+of+model+categories">Bousfield localization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/transferred+model+structure">transferred model structure</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/model+structure+on+algebraic+fibrant+objects">on algebraic fibrant objects</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Grothendieck+construction+for+model+categories">Grothendieck construction for model categories</a> </li> </ul> Presentation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>∞</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\infty,1)</annotation></semantics></math>-categories <ul> <li> <a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2C1%29-category">(∞,1)-category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/simplicial+localization">simplicial localization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2C1%29-categorical+hom-space">(∞,1)-categorical hom-space</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/presentable+%28%E2%88%9E%2C1%29-category">presentable (∞,1)-category</a> </li> </ul> Model structures <ul> <li><a class="existingWikiWord" href="/nlab/show/Cisinski+model+structure">Cisinski model structure</a></li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groupoids <a class="existingWikiWord" href="/nlab/show/model+structure+for+%E2%88%9E-groupoids">for ∞-groupoids</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+topological+spaces">on topological spaces</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/classical+model+structure+on+topological+spaces">classical model structure</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+compactly+generated+topological+spaces">on compactly generated spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+Delta-generated+topological+spaces">on Delta-generated spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+diffeological+spaces">on diffeological spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Str%C3%B8m+model+structure">Strøm model structure</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Thomason+model+structure">Thomason model structure</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+presheaves+over+a+test+category">model structure on presheaves over a test category</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+sets">on simplicial sets</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+on+semi-simplicial+sets">on semi-simplicial sets</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/classical+model+structure+on+simplicial+sets">classical model structure</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/constructive+model+structure+on+simplicial+sets">constructive model structure</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+right+fibrations">for right/left fibrations</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+groupoids">model structure on simplicial groupoids</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+cubical+sets">on cubical sets</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+strict+%E2%88%9E-groupoids">on strict ∞-groupoids</a>, <a class="existingWikiWord" href="/nlab/show/natural+model+structure+on+groupoids">on groupoids</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+chain+complexes">on chain complexes</a>/<a class="existingWikiWord" href="/nlab/show/model+structure+on+cosimplicial+abelian+groups">model structure on cosimplicial abelian groups</a> related by the <a class="existingWikiWord" href="/nlab/show/Dold-Kan+correspondence">Dold-Kan correspondence</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+cosimplicial+simplicial+sets">model structure on cosimplicial simplicial sets</a> </li> </ul> for equivariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groupoids <ul> <li> <a class="existingWikiWord" href="/nlab/show/fine+model+structure+on+topological+G-spaces">fine model structure on topological G-spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/coarse+model+structure+on+topological+G-spaces">coarse model structure on topological G-spaces</a> (<a class="existingWikiWord" href="/nlab/show/Borel+model+structure">Borel model structure</a>) </li> </ul> for rational <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groupoids <ul> <li><a class="existingWikiWord" href="/nlab/show/model+structure+on+dgc-algebras">model structure on dgc-algebras</a></li> </ul> for rational equivariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groupoids <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+equivariant+chain+complexes">model structure on equivariant chain complexes</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+equivariant+dgc-algebras">model structure on equivariant dgc-algebras</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>-groupoids <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+n-groupoids">for n-groupoids</a>/<a class="existingWikiWord" href="/nlab/show/model+structure+for+n-groupoids">for n-types</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/canonical+model+structure+on+groupoids">for 1-groupoids</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groups <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+groups">model structure on simplicial groups</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+reduced+simplicial+sets">model structure on reduced simplicial sets</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-algebras general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-algebras <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+monoids">on monoids</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+T-algebras">on simplicial T-algebras</a>, on <a class="existingWikiWord" href="/nlab/show/homotopy+T-algebra">homotopy T-algebra</a>s </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+algebras+over+a+monad">on algebas over a monad</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+algebras+over+an+operad">on algebras over an operad</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+on+modules+over+an+algebra+over+an+operad">on modules over an algebra over an operad</a> </li> </ul> specific <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-algebras <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-algebras">model structure on differential-graded commutative algebras</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+differential+graded-commutative+superalgebras">model structure on differential graded-commutative superalgebras</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-algebras+over+an+operad">on dg-algebras over an operad</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-algebras">on dg-algebras</a> and on <a class="existingWikiWord" href="/nlab/show/simplicial+ring">on simplicial rings</a>/<a class="existingWikiWord" href="/nlab/show/model+structure+on+cosimplicial+rings">on cosimplicial rings</a> related by the <a class="existingWikiWord" href="/nlab/show/monoidal+Dold-Kan+correspondence">monoidal Dold-Kan correspondence</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+L-%E2%88%9E+algebras">for L-∞ algebras</a>: <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-Lie+algebras">on dg-Lie algebras</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-coalgebras">on dg-coalgebras</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+Lie+algebras">on simplicial Lie algebras</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-modules">model structure on dg-modules</a> </li> </ul> for stable/spectrum objects <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+spectra">model structure on spectra</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+ring+spectra">model structure on ring spectra</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+parameterized+spectra">model structure on parameterized spectra</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+presheaves+of+spectra">model structure on presheaves of spectra</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>∞</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\infty,1)</annotation></semantics></math>-categories <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+categories+with+weak+equivalences">on categories with weak equivalences</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+quasi-categories">Joyal model for quasi-categories</a> (and its <a class="existingWikiWord" href="/nlab/show/model+structure+for+cubical+quasicategories">cubical version</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+sSet-categories">on sSet-categories</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+complete+Segal+spaces">for complete Segal spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+Cartesian+fibrations">for Cartesian fibrations</a> </li> </ul> for stable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>∞</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\infty,1)</annotation></semantics></math>-categories <ul> <li><a class="existingWikiWord" href="/nlab/show/model+structure+on+dg-categories">on dg-categories</a></li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>∞</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\infty,1)</annotation></semantics></math>-operads <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+operads">on operads</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+for+Segal+operads">for Segal operads</a> <a class="existingWikiWord" href="/nlab/show/model+structure+on+algebras+over+an+operad">on algebras over an operad</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+on+modules+over+an+algebra+over+an+operad">on modules over an algebra over an operad</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+dendroidal+sets">on dendroidal sets</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+for+dendroidal+complete+Segal+spaces">for dendroidal complete Segal spaces</a>, <a class="existingWikiWord" href="/nlab/show/model+structure+for+dendroidal+Cartesian+fibrations">for dendroidal Cartesian fibrations</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(n,r)</annotation></semantics></math>-categories <ul> <li> <a class="existingWikiWord" href="/nlab/show/Theta+space">for (n,r)-categories as ∞-spaces</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+weak+complicial+sets">for weak ∞-categories as weak complicial sets</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+cellular+sets">on cellular sets</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/canonical+model+structure">on higher categories in general</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+strict+%E2%88%9E-categories">on strict ∞-categories</a> </li> </ul> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">(</mo><mn>∞</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\infty,1)</annotation></semantics></math>-sheaves / <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-stacks <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+homotopical+presheaves">on homotopical presheaves</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+presheaves">on simplicial presheaves</a> <a class="existingWikiWord" href="/nlab/show/global+model+structure+on+simplicial+presheaves">global model structure</a>/<a class="existingWikiWord" href="/nlab/show/Cech+model+structure+on+simplicial+presheaves">Cech model structure</a>/<a class="existingWikiWord" href="/nlab/show/local+model+structure+on+simplicial+presheaves">local model structure</a> <a class="existingWikiWord" href="/nlab/show/model+structure+on+simplicial+sheaves">on simplicial sheaves</a> <a class="existingWikiWord" href="/nlab/show/model+structure+on+presheaves+of+simplicial+groupoids">on presheaves of simplicial groupoids</a> <a class="existingWikiWord" href="/nlab/show/model+structure+on+sSet-enriched+presheaves">on sSet-enriched presheaves</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+structure+for+%282%2C1%29-sheaves">model structure for (2,1)-sheaves</a>/for stacks </li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#references'>References</a></li> </ul> </div> <h2 id="idea">Idea</h2> There is a <a class="existingWikiWord" href="/nlab/show/cofibrantly+generated+model+category">cofibrantly generated</a> (“<a class="existingWikiWord" href="/nlab/show/folk+model+structure">folk</a>”) <a class="existingWikiWord" href="/nlab/show/model+category">model structure</a> on the category of <a class="existingWikiWord" href="/nlab/show/strict+%E2%88%9E-groupoid">strict ∞-groupoid</a>s, equivalently that of <a class="existingWikiWord" href="/nlab/show/crossed+complex">crossed complex</a>es. It is the <a class="existingWikiWord" href="/nlab/show/transferred+model+structure">transferred model structure</a> along the <a class="existingWikiWord" href="/nlab/show/forgetful+functor">forgetful functor</a> of the <a class="existingWikiWord" href="/nlab/show/model+structure+on+strict+%E2%88%9E-categories">model structure on strict ∞-categories</a>. <h2 id="references">References</h2> The model structure was given in <ul id="BrownGolasinski"> <li><a class="existingWikiWord" href="/nlab/show/Ronnie+Brown">Ronnie Brown</a>, <a class="existingWikiWord" href="/nlab/show/Marek+Golasinski">Marek Golasinski</a>; A model structure for the homotopy theory of crossed complexes (<a href="http://www.numdam.org/numdam-bin/fitem?id=CTGDC_1989__30_1_61_0">numdam</a>) Cahiers Topologie Géom. Différentielle 30 (1989) 61-82.</li> </ul> The relation to the model structure on strict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math>-categories was established in <ul id="AraMetayer"> <li>Dimitri Ara, <a class="existingWikiWord" href="/nlab/show/Francois+Metayer">Francois Metayer</a>, The Brown-Golasinski model structure on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>∞</mn></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>-groupoids revisited (<a href="http://hal.archives-ouvertes.fr/docs/00/52/58/42/PDF/folkgr.pdf">pdf</a>) Homology, Homotopy Appl. 13 (2011), no. 1, 121–142.</li> </ul> </body></html> </div> <div class="revisedby"> Last revised on January 20, 2015 at 12:57:26. 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