Homotopy colimit III 给出了范畴Top中同伦余极限的构造,这一篇文章就做个对偶,构造一下同伦极限并给出几个例子。 给定一个余单纯空间X:Δ→Top,它的全部化(totalisation)定义为 Tot(X):=eq[∏[n]XnΔn⇉∏[n]→[k]XkΔn]. 回顾上一篇文章中几何实现的定义,这里就是“把所有的co去掉了”(同样地函...
Homotopy Colimit IV 一罐鱼 11 人赞同了该文章 好的,结束了范畴 Top 中的同伦极限、余极限的构造,接下来对构造性的定义进行公理化,来解释“同伦余极限是余极限的导出函子”。这并不是一个容易的事情,但幸好在此之前人们(Quillen)已经在这个方向做出了许多有意义的努力。 进入正题之前先提一点关于导出函子的...
Our results extend to homotopy colimits of 2-functors lower categorical analogues that have been classically used in algebraic topology and algebraic K-theory, such as the Homotopy Invariance Theorem (by Bousfield and Kan), the Homotopy Colimit Theorem (Thomason), Theorems A and B (Quillen), ...
·genus,TheoremofGauss-Bonnetχ(M)=12π McurvaturedAforManycompact2-dimensionalRiemannianmanifold.IntroductionFinitenessObstructionsandEulerCharacteristicsforCategoriesClassifyingI-SpacesHomotopyColimitFormulaandtheInclusion-ExclusionPrincipleComparisonwithLeinster’sNotionsApplicationsandSummaryIntroductionProblem:meaningfully...
Abstract In this note we give a model category theoretic interpretation of the homotopy colimit of the diagram of simplicial localizations coming from a diagram of model categories in the case of an inverse indexing category.Previous article in issue Next article in issue...
HOMOTOPY (LIMITS AND) COLIMITS For model categories, we define a homotopy colimit functor to be a derived functor of the usual colimit functor. Finally, we note that in the set- ting of a simplicial model category, these two approaches coincide and refer the ... E Riehl 被引量: 2发表...
We have an inverse system of cofibre sequences Sign in to download full-size image which induces a direct system of long exact sequences Sign in to download full-size image The limit of these is a long exact sequence of the form ⋯→πk(Y)→p−1πk(Y)→πk(Y)/(p∞)→⋯ ...
stheoremasastartingpointtostudyhomotopylimitsfor2-categories.Ourfirststepistoshowthatforeverysmall2-categoryAandevery2-categoryKwithfinitelimitsandsmallcolimits,thefunctor2-category[A,K]admitsamodelstructureinwhichtheweakequivalencesarethepointwiseequivalencesandthefibrationsarethepointwiseisofibrations....
The dg A-module LA can be represented as a homotopy inverse limit of its Postnikov tower {LA[n]:n=0,1,…}{LA[n]:n=0,1,…} (so that LA[n]LA[n] has the same homology as LA up to and including degree n and zero in higher degrees). The homotopy cofibers LA...
From the ColimitTheorem for the Fundamental Crossed Complex of a CW-complex (due to R. Brownand P.J. Higgins), follows an algebraic analogue for the fundamental crossedcomplex $\\Pi(M)$ of the skeletal filtration of $M$, which thus depends only onthe homotopy type of $M$ (as a ...