Generalizing Morita duality: A homological approach

Let R and S be arbitrary associative rings. Given a bimodule RWS, we denote by ∆? and Γ? the functors Hom?(−,W) and Ext1?(−,W), where ? = R or S. The functors ∆R and ∆S are right adjoint with the evaluation maps δ as unities. A module M is ∆-reflexive if δM is an isomorphism. In this paper we give, for a weakly cotilting bimodule RWS, the notion of Γ-reflexivity. We construct large abelian subcategories MR and MS where the functors ΓR and ΓS are left adjoint and a “Cotilting theorem” holds.