The subobject decomposition in enveloping tensor categories

Abstract

To every regular category A equipped with a degree function δ one can attach a pseudo-abelian tensor category T(A,δ). We show that the generating objects of T decompose canonically as a direct sum. In this paper we calculate morphisms, compositions of morphisms and tensor products of the summands. As a special case we recover the original construction of Deligne’s category RepSt.