GENERALIZING A DEFINITION OF LUSTERNIK AND SCHNIRELMANN TO MODEL CATEGORIES

[摘要] Lusternik-Schnirelmann category is an important numerical homotopy invariant, defined originally for topological spaces but employed since in other categories in which there is a good notion of homotopy. In the interest of unification, Doeraene defined a J-category to be a category satisfying a certain set of axioms which ensure that an LS-type invariant can be reasonably defined. He provided two equivalent definitions of LS-category for J-categories and showed that these generalized definitions agree with previous definitions in specific categories. Extending his results, we provide a third equivalent definition of the LS-category of an object in a J-category, analogous to the original topological definition of Lusternik and Schnirelmann.

[发布日期] 1994-01-17