Generalizing morita duality: A homological approach

Let R and S be arbitrary associative rings. Given a bimodule (R)W(S), we denote by Delta(?) and Gamma(?) the functors Hom(?)(-, W) and Ext(?)(1)(-, W), where ? = R or S. The functors Delta(R) and Delta(S) are right adjoint with the evaluation maps delta as unities. A module M is Delta-reflexive if delta(M) is an isomorphism. In this paper we give, for a weakly cotilting bimodule (R)W(S) the notion of Gamma-reflexivity. We construct large Abelian subcategories M(R) and M(S) where the functors Gamma(R) and Gamma(S) are left adjoint and a "cotilting theorem" holds. (C) 2000 Academic Press.