The Auslander-Reiten duality via morphisms determined by objects

Given an exact category C, we denote by Cl the smallest additive subcategory containing injectives and indecomposable objects which appear as the first term of an almost split conflation. We prove that a deflation is right determined by some object if and only if its intrinsic kernel lies in Cl. We give characterizations for C having Auslander-Reiten duality.