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...
最后虽然我们可以直接证明 \mathrm{colim}~QX\cong\mathrm{hocolim}~X ,但有更合适的工具来证明这个事情,希望之后不久就可以讨论到。 虽然当范畴是 \bm{\mathrm{Top}} 时我们证明了 \mathrm{hocolim}~X 是导出函子,但对其他范畴的讨论并不轻松,不同的(模型)范畴会遇到不同的问题,因此同伦余极限公理化的工...
Categorical tools for homotopy (co)limit computationsEmily Riehl
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...
In either case, Y is a subspace of Cf, and the evident inclusion map will be denoted by i. The following result is an elementary exercise. PROPOSITION 3.3.2 Let i: Y→ Cf be the map given by 3.3.1. Then Ci is homotopy equivalent to ΣX. DEFINITION 3.3.3 A cofibre sequence is ...
Homotopy limits of model categories and more general homotopy theories 来自 国家科技图书文献中心 喜欢 0 阅读量: 43 作者: JE Bergner 摘要: Generalizing a definition of homotopy fiber products of model categories, we give a definition of the homotopy limit of a diagram of left Quillen ...
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 ...
Equivalently, f is acyclic if an only if it induces a Verdier localization of the triangulated categories of cohomologically locally constant sheaves (also known as infinity local systems) on X and Y . Finally, we consider, for a given connected space X, its p-plus-construction X+pXp+; ...
stheoremasastartingpointtostudyhomotopylimitsfor2-categories.Ourfirststepistoshowthatforeverysmall2-categoryAandevery2-categoryKwithfinitelimitsandsmallcolimits,thefunctor2-category[A,K]admitsamodelstructureinwhichtheweakequivalencesarethepointwiseequivalencesandthefibrationsarethepointwiseisofibrations....
One of the main advantages to a theory of higher categories, is that the notions of homotopy limit and homotopy colimit, by now classical in algebra... JP Pridham - 《Proceedings of the London Mathematical Society》 被引量: 45发表: 2008年 Convenient categories of topological spaces for homoto...