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 [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.
Keywords: general linear groupoid; finite field; monoid representation; Joyal species; Morita equivalence; Dold-Kan-type theorems
2020 MSC: 20C33; 16D90; 18M80; 20L05; 18A32; 18B40; 18D60
Theory and Applications of Categories, Vol. 41, 2024, No. 21, pp 686-706.
Published 2024-06-19.
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