The Drinfeld center of an oligomorphic tensor category

TL;DR

This paper develops methods to analyze the Drinfeld centers of oligomorphic tensor categories, explicitly computes some cases, and identifies new categories that are their own centers, expanding understanding of pre-Tannakian categories.

Contribution

It introduces tools for studying Drinfeld centers of oligomorphic tensor categories and finds new examples of categories that are equivalent to their own centers.

Findings

Explicit computation of Drinfeld centers in several cases

Identification of categories that are their own centers

Discovery of new finitely tensor-generated pre-Tannakian categories

Abstract

Recently, Harman and the second author introduced a new construction of pre-Tannakian tensor categories based on oligomorphic groups. We develop tools for analyzing the Drinfeld centers of these categories, and compute the center explicitly in a number of cases. In particular, we find several finitely tensor-generated pre-Tannakian categories (including the Delannoy category) that are identified with their own center via the canonical functor; prior to this work, we knew no such examples besides the category of vector spaces.