Barker, L.Demirel, M.2018-04-122018-04-1220161386-923Xhttp://hdl.handle.net/11693/36926Generalizing an idea used by Bouc, Thévenaz, Webb and others, we introduce the notion of an admissible R-linear category for a commutative unital ring R. Given an R-linear category (Formula presented.) , we define an (Formula presented.) -functor to be a functor from (Formula presented.) to the category of R-modules. In the case where (Formula presented.) is admissible, we establish a bijective correspondence between the isomorphism classes of simple functors and the equivalence classes of pairs (G, V) where G is an object and V is a module of a certain quotient of the endomorphism algebra of G. Here, two pairs (F, U) and (G, V) are equivalent provided there exists an isomorphism F ← G effecting transport to U from V. We apply this to the category of finite abelian p-groups and to a class of subcategories of the biset category. © 2015, Springer Science+Business Media Dordrecht.EnglishBiset categoryGroup categoryQuiver algebra of a linear categorySeeds of simple functorsEquivalence classesGroup theorySet theoryBiset categoryFunctorsGroup categoryIsomorphism classLinear categoriesp-GroupAlgebraPrimary: 20C20Secondary: 20J99Article10.1007/s10468-015-9583-21572-9079