Journal of the
Korean Mathematical Society JKMS

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.

Keywords: Lusternik-Schnirelmann category, cocategory, rational category, rational cocategory, rational fibration, left-versal, right-versal, fiber-length

MSC numbers: 55M30, 55P30, 55U35