  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.
