The subobject decomposition in enveloping tensor categories
arXiv:2103.08686 · doi:10.1016/j.indag.2021.12.008
Abstract
To every regular category equipped with a degree function one can attach a pseudo-abelian tensor category . We show that the generating objects of 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 .
v1: 16 pages; v2: 16 pages, typos fixed, comparison with Deligne's construction extended; v3: 16 pages, a few typos corrected, final version, to appear in a memorial volume for T.A. Springer