Mappings of bar constructions
type: Item
instance of: scholarly article
title: Mappings of bar constructions
zbMATH Open document ID: 0587.55013
DOI: 10.1007/BF02760632
author: Jean-Pierre Meyer
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The author generalizes Quillen's theorems A and B [\textit{D. G. Quillen}, Lect. Notes Math. 341, 85-147 (1973; Zbl 0292.18004)] describing homotopy properties of the induced mapping Bf: B\({\mathcal C}\to B{\mathcal C}'\) where \(f: {\mathcal C}\to {\mathcal C}'\) is a functor and B is the classifying space functor to bar constructions in the category Top of topological spaces. Further generalizations in the spirit of the author [J. Pure Appl. Algebra 33, 163-207 (1984; Zbl 0542.57036)] where for instance Top is replaced by a suitable category with homotopy are announced.
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55R05
Mathematics Subject Classification ID: 57T30
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 3942508
zbMATH Keywords: homotopy fibre
zbMATH Keywords: homotopy equivalence
zbMATH Keywords: classifying space functor
zbMATH Keywords: bar constructions
MaRDI profile type: Publication
cites work: Homotopy limits, completions and localizations
cites work: Classifying spaces and fibrations
cites work: Bar and cobar constructions. I
cites work: Bar and cobar constructions. II
cites work: Construction of universal bundles. II
cites work: Q4166884
cites work: A remark on 'homotopy fibrations'
cites work: Higher algebraic K-theory: I
cites work: Classifying spaces and spectral sequences
cites work: Associated fibre spaces
cites work: Homotopy colimits in the category of small categories
cites work: Quasifibration and adjunction
full work available at URL: https://doi.org/10.1007/bf02760632
OpenAlex ID: W2055127129
description: scientific article; zbMATH DE number 3942508