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- Title
Simple Functors of Admissible Linear Categories.
- Authors
Barker, Laurence; Demirel, Merve
- Abstract
Generalizing 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 $\mathcal {L}$ , we define an $\mathcal {L}$ -functor to be a functor from $\mathcal {L}$ to the category of R-modules. In the case where $\mathcal {L}$ 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.
- Publication
Algebras & Representation Theory, 2016, Vol 19, Issue 2, p463
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-015-9583-2