Adjoint functors and equivalences of subcategories

Abstract

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S − and Hom R ( P,−) induce an equivalence between the categories of P-static R-modules and P-adstatic S-modules. In particular, this setting subsumes the Morita theory of equivalences between module categories and the theory of tilting modules. In this paper we consider, more generally, any adjoint pair of covariant functors between complete and cocomplete Abelian categories and describe equivalences induced by them. Our results subsume the situations mentioned above but also equivalences between categories of comodules.