The core groupoid can suffice

This work results from a study of Nicholas Kuhn's paper entitled "Generic representation theory of finite fields in nondescribing characteristic". Our goal is abstract the categorical structure required to obtain an equivalence between functor categories [F, V] and [G, V] where G is the core groupoid of the category F and V is a category of modules over a commutative ring. Examples other than Kuhn's are covered by this general setting.