Model category extensions of the Pirashvili-Słomińska theorems

Details Model category extensions of the Pirashvili-Słomińska theorems Model category extensions of the Pirashvili-Słomińska theorems

2008-06-10

arxiv.org/abs/0806.1540v1

Mathematics

Category Theory

27 pages, submitted to Journal of Homotopy and Related Structures

Scientific paper

We describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We provide a construction of pairs of small categories--known as conjugate pairs--whose associated categories of diagrams are Quillen equivalent in the semi-stable setting. We frame our development in the context of Morita theory, following Slominska's work on similar questions for categories of functors enriched over and taking values in R-modules.

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