[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2002.39.2.163

CLAPP-PUPPE TYPE LUSTERNIK-SCHNIRELMANN (CO)CATEGORY IN A MODEL CATEGORY

Yau, Donald (Department of Mathematics, Massachusetts Institute of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.39, no.2, 2002 , pp. 163-191 More about this Journal

Abstract

We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category in a Quillen model category. We establish some of their basic properties and give various characterizations of them. As the first application of these characterizations, we show that our generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category is invariant under Quillen modelization equivalences. In particular, generalized (co)category of spaces and simplicial sets coincide. Another application of these characterizations is to define and study rational cocategory. Various other applications are also given.

Keywords

Lusternik-Schnirelmann category; cocategory; rational category; rational cocategory; rational fibration; left-versal; right-versal; fiber length;

Citations & Related Records

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