Clapp-Puppe Type Lusternik-Schnirelmann (Co)category in a Model Category

Details Clapp-Puppe Type Lusternik-Schnirelmann (Co)category in a Model Category Clapp-Puppe Type Lusternik-Schnirelmann (Co)category in a Model Category

2001-04-27

arxiv.org/abs/math/0104267v1

Mathematics

Algebraic Topology

To appear in J. Korean Math. Soc

Scientific paper

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 of spaces and simplicial sets coincide. Another application of these characterizations is to define and study rational cocategory. Various other applications are also given.

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