Homotopy limits of categories
type: Item
instance of: scholarly article
title: Homotopy limits of categories
zbMATH Open document ID: 0815.18007
DOI: 10.1016/0022-4049(93)00008-S
author: Manos G. Lydakis
published in: Journal of Pure and Applied Algebra
publication date: 1995-06-12T00:00:00Z
review text: Given a diagram \(A : {\mathcal I} \to {\mathcal C}at\) of small categories, \textit{R. W. Thomason} [Math. Proc. Cambridge Philos. Soc. 85, 91-109 (1979; Zbl 0392.18001)] proved that the Grothendieck construction \({\mathcal I} \int A\) is a category with nerve homotopically equivalent to hocolim NA, the homotopy colimit of NA, the corresponding diagram of simplicial sets obtained by applying the nerve to \(A\). Considering holim NA, the homotopy limit of \(A\), the author proves that it is isomorphic to the nerve of a category and uses this to prove a weak form of the Bousfield-Kan cofinality theorem.
reviewed by: Timothy Porter
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 719443
zbMATH Keywords: nerve of category
zbMATH Keywords: Grothendieck construction
zbMATH Keywords: homotopy colimit
zbMATH Keywords: simplicial sets
zbMATH Keywords: Bousfield-Kan cofinality theorem
MaRDI profile type: Publication
cites work: Homotopy limits, completions and localizations
cites work: Adjoint Functors
cites work: Fixed point problems, equivariant stable homotopy, and a trace map for the algebraic \(K\)-theory of a point
cites work: Classifying spaces and spectral sequences
cites work: Homotopy colimits in the category of small categories
description: scientific article; zbMATH DE number 719443