On the homotopy structure of strongly homotopy associative algebras
type: Item
instance of: scholarly article
title: On the homotopy structure of strongly homotopy associative algebras
zbMATH Open document ID: 0923.18007
DOI: 10.1016/S0022-4049(97)00143-6
author: Marco Grandis
published in: Journal of Pure and Applied Algebra
publication date: 1999-10-18T00:00:00Z
review text: Let \({\mathcal S}{\mathcal H}{\mathcal A}\) be the category of strongly homotopy associative algebras and strongly homotopy multiplicative maps. This category was first considered by \textit{J. D. Stasheff} [Trans. Am. Math. Soc. 108, 275-292, 293-312 (1963; Zbl 0114.39402)] for the study of singular chain complexes of loop spaces. The author investigates the homotopy structure of the category \({\mathcal S}{\mathcal H}{\mathcal A}\). In particular, he shows that the cocylinder functor of \({\mathcal D}{\mathcal H}{\mathcal A}\) is extended to \({\mathcal S}{\mathcal H}{\mathcal A}\) and that homotopy pullbacks exist in \({\mathcal S}{\mathcal H}{\mathcal A}\).
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 1308287
zbMATH Keywords: strong homotopy
zbMATH Keywords: associative differential algebra
zbMATH Keywords: associative algebra
reviewed by: Kohhei Yamaguchi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308287