An \(E^ 2\) model category structure for pointed simplicial spaces
type: Item
instance of: scholarly article
title: An \(E^ 2\) model category structure for pointed simplicial spaces
zbMATH Open document ID: 0814.55008
DOI: 10.1016/0022-4049(93)90126-E
published in: Journal of Pure and Applied Algebra
publication date: 1994-03-10T00:00:00Z
review text: The \(E^ 2\) model category structure in the title is a new closed simplicial model category structure in the sense of \textit{D. G. Quillen} [Homotopical algebra, Lect. Notes Math. 43 (1967; Zbl 0168.209)] on the category \(s{\mathbf T}_ *\), of simplicial objects over the category, \({\mathbf T}_ *\), of pointed topological spaces. Such a structure allows one to define the notion of a (homotopy-theoretic) resolution of a topological space by simplicial spaces and gives rise to the notion of equivalence of resolutions. The \(E^ 2\) model category structure specifies a larger class of weak equivalences than a similar structure due to \textit{C. L. Reedy} [Homotopy theory of model categories] does. This means that greater flexibility in choosing homotopy-theoretic resolutions is available. The \(E^ 2\) terminology is justified by the fact that a map between simplicial objects is a weak equivalence if and only if it induces an isomorphism on \(E^ 2\)-terms of a certain spectral sequence.
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 500590
zbMATH Keywords: simplicial objects over the category of pointed topological spaces
zbMATH Keywords: closed simplicial model category
zbMATH Keywords: resolution of a topological space
zbMATH Keywords: weak equivalences
zbMATH Keywords: spectral sequence
author: William Dwyer
author: D. M. Kan
author: Christopher R. Stover
reviewed by: Klaus Heiner Kamps
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 500590