Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLAPP-PUPPE TYPE LUSTERNIK-SCHNIRELMANN (CO)CATEGORY IN A MODEL CATEGORY

  • Yau, Donald (Department of Mathematics, Massachusetts Institute of Technology)
  • Published : 2002.03.01
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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.

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