The core groupoid can suffice

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Abstract
This work results from a study of Nicholas Kuhn's paper entitled "Generic representation theory of finite fields in nondescribing characteristic". Our goal is to abstract the categorical structure required to obtain an equivalence between functor categories rF , V s and rG , V s 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.