The Auslander-Reiten duality via morphisms determined by objects

Given an exact category $\mathcal{C}$, we denote by $\mathcal{C}_l$ 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 $\mathcal{C}_l$. We give characterizations for $\mathcal{C}$ having Auslander-Reiten duality.