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Topology/Geometry Seminar
Thursday, November 18, 2004
5:30-7:00pm,
209 Holt (Altoona)
Randall Helmstutler
Washington and Lee University, VA
A Morita theory for stable model categories
Abstract: The general question we consider is that of equivalences of categories of functors (also know as categories of diagrams). Our primary focus is on contravariant functors taking values in an arbitrary stable modelcategory. We describe certain conditions on a pair (A, B) of small categories that ensure that the categories of contravariant diagrams indexed by A and those indexed by B are Quillen equivalent. As an important example, our theorem applies to the following two categories: the category of finite based sets, and the category of (unbased) sets and epimorphisms. This example arises in N. Kuhn's generalization of the $SP^\infty$ construction to good categories of spectra, as well as in the use of cross effects in the Goodwillie calculus. Finally, we remark that all of our results hold if the stable model category is replaced by any abelian category.
