Generalizing a definition of Lusternik and Schnirelmann to model categories
type: Item
instance of: scholarly article
title: Generalizing a definition of Lusternik and Schnirelmann to model categories
zbMATH Open document ID: 0790.55007
DOI: 10.1016/0022-4049(94)90140-6
author: Jean-Michel Lemaire
author: Kathryn Hess
published in: Journal of Pure and Applied Algebra
publication date: 1994-06-26T00:00:00Z
review text: This paper has to be considered as a sequel to the paper of \textit{J. P. Doeraene} concerning the definition of a Lusternik-Schnirelmann category in a \(J\)-category [ibid. 84, 215-261 (1993; Zbl 0777.55007)]. The authors give a new definition of the L. S. category that is more analogous to the original topological definition of Lusternik and Schnirelmann. This definition is proved to be equivalent to the Doeraene's original one. With this definition, the authors give a new (and more direct) proof for the following result: Let \(f: A\to B\) be a morphism in a \(J\)-category. Denote by \(C_ f\) the cofibre, then \(\text{cat } C_ f\leq \text{cat } B+1\).
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 500570
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: closed model category
zbMATH Keywords: rational homotopy theory
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90140-6
OpenAlex ID: W1965091588
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description: scientific article; zbMATH DE number 500570