The categories of \(A_{\infty}\) and \(E_{\infty}\)-monoids and ring spaces as closed simplicial and topological model categories
type: Item
instance of: scholarly article
title: The categories of \(A_{\infty}\) and \(E_{\infty}\)-monoids and ring spaces as closed simplicial and topological model categories
zbMATH Open document ID: 0733.55008
DOI: 10.1007/BF01198229
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: The authors deduce, by means of \textit{D. G. Quillen}'s [Homotopical algebra, (Lect. Notes Math. 43) (1967; Zbl 0168.209)] and \textit{W. G. Dwyer} and \textit{D. M. Kan}'s [Indag. Math. 46, 147-153 (1984; Zbl 0555.55019)] results, a closed topological model category structure on the category of \(\theta\)-spaces [\textit{J. M. Boardman} and \textit{R. M. Vogt}, Homotopy invariant algebraic structures on topological spaces (Lect. Notes Math. 347) (1973; Zbl 0285.55012)]. Then, closed simplicial and topological model category structures on the categories of \(A_{\infty}\)- resp. \(E_{\infty}\)-monoids or ring spaces are obtained.
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 4213007
zbMATH Keywords: closed model category
zbMATH Keywords: \(\theta \) -spaces
zbMATH Keywords: \(A_{\infty }\)- resp. \(E_{\infty }\)-monoids
zbMATH Keywords: ring spaces
author: Roland Schwänzl
author: Rainer Vogt
reviewed by: Marek Golasiński
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01198229
OpenAlex ID: W1969873165
description: scientific article; zbMATH DE number 4213007