On a finitistic cotilting-type duality

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. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W, finitely generated or homomorphic image of a finite direct sum of copies of W, ΓM = 0 = Ext2(M,W). We are able to describe, on a large class of finitely generated modules, the cotilting- type duality induced by a FWC-bimodule.