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.
Generalizing Morita duality: A homological approach
TONOLO, ALBERTO
2000
Abstract
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.File in questo prodotto:
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