  We study the existence and uniqueness of minimal right determiners in various
categories. Particularly in a Hom-finite hereditary abelian category with
enough projectives, we prove that the Auslander-Reiten-Smal{\o}-Ringel formula
of the minimal right determiner still holds. As an application, we give a
formula of minimal right determiners in the category of finitely presented
representations of strongly locally finite quivers.
