A generalization of Morita Duality by Localizations

Abstract

Let R and S be rings with identity, and Mod-R and S-Mod the category of unital right R- and left S-modules, respectively. Also let A and B be full subcategories of Mod-R and S-Mod such that A〓R and B〓S and both are closed under finite direct sums, submodules and epimomorphic images. We will find conditions in order that there exists a duality between Giraud subcategories of A and B. As an application of this we will obtain a general result of [8] about Morita duality between Grothendieck categories.