Bar and cobar constructions. II
type: Item
instance of: scholarly article
title: Bar and cobar constructions. II
zbMATH Open document ID: 0625.57024
DOI: 10.1016/0022-4049(86)90094-0
author: Jean-Pierre Meyer
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: The author [Isr. J. Math. 48, 331-339 (1984; Zbl 0587.55013)] generalized Quillen's Theorems A and B on homotopy properties of the classical classifying space functor [see \textit{D. Quillen}, Lect. Notes Math. 341, 85-147 (1973; Zbl 0292.18004)] to bar constructions in the category \({\mathcal T}op\) of topological spaces. Further generalizations were announced in that paper. These generalizations are carried out in the present paper. The main points are that the category \({\mathcal T}op\) is replaced by a suitable category with homotopy and that homotopy equivalences or quasi-fibrations are replaced by more general families of morphisms. The resulting main theorem (Quillen's theorem B for bar constructions) of the paper covers a great number of existing results on homotopy limits and classifying spaces due to Bousfield-Kan, May, Milgram, Stasheff et al. As a matter of independent interest a general theory of geometrical realizations begun in the first part of the paper [the author, J. Pure Appl. Algebra 33, 163-207 (1984; Zbl 0542.57036)] is continued in the present paper.
Mathematics Subject Classification ID: 57T30
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 55P10
zbMATH DE Number: 4015737
zbMATH Keywords: category of topological spaces
zbMATH Keywords: bar constructions
zbMATH Keywords: category with homotopy
zbMATH Keywords: homotopy limits
zbMATH Keywords: classifying spaces
zbMATH Keywords: geometrical realizations
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90094-0
OpenAlex ID: W4212993358
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description: scientific article; zbMATH DE number 4015737