Universal rigid abelian tensor categories and Schur finiteness

TL;DR

This paper investigates the structure of Schur-finite rigid tensor categories, providing foundational insights into their ideal structure and extending the construction of certain algebraic categories.

Contribution

It offers a detailed study of the construction of rigid abelian tensor categories, focusing on Schur-finiteness and their ideal structures, advancing the theoretical framework.

Findings

Detailed analysis of Schur-finite rigid tensor categories

Foundational groundwork on ideal structures in tensor categories

Extension of previous constructions in algebraic category theory

Abstract

We study the construction of arXiv:2111.11217 [math:AG] in more detail, especially in the case of Schur-finite rigid $\otimes$-categories. This leads to some groundwork on the ideal structure of rigid additive and abelian $\otimes$-categories.