Simple functors of admissible linear categories

Abstract

We review the notion of an admissible R-linear category for a commutative unital ring R and we prove the classification theorem for simple functors of such a category by Barker-Boltje which states that there is a bijective correspondence between the seeds of linear category and simple linear functors. We also review the application of this theorem by Bouc to the biset category by showing that the biset category is admissible. Finally, we classify the simple functors for the category of finite abelian p-groups and show that, for a natural number n, the n-th simple functor is non-zero on precisely the groups which have exponent at least pn .