Generalizing a definition of Lusternik and Schnirelmann to model categories (Q1313782)

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 \(\text{cat } C_ f\leq \text{cat } B+1\).