The core groupoid can suffice

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 $[\mathcal{F},\mathcal{V}]$ and $[\mathcal{G},\mathcal{V}]$ where $\mathcal{G}$ is the core groupoid of the category $\mathcal{F}$ and $\mathcal{V}$ is a category of modules over a commutative ring.

This version includes further examples, remarks and references following feedback on version 1 from Benjamin Steinberg