Multifusion Categories and Finite Semisimple 2-Categories

TL;DR

This paper establishes a universal property for the Karoubi envelope of a 2-category and proves the equivalence between finite semisimple 2-categories and multifusion categories, advancing the understanding of higher categorical structures.

Contribution

It introduces a 3-universal property for the Karoubi envelope and demonstrates the equivalence between finite semisimple 2-categories and multifusion categories.

Findings

Karoubi envelope has a 3-universal property

Finite semisimple 2-categories are equivalent to multifusion categories

Advances the categorical understanding of multifusion structures

Abstract

We give a 3-universal property for the Karoubi envelope of a 2-category. Using this, we show that the 3-categories of finite semisimple 2-categories (as introduced in arXiv:1812.11933) and of multifusion categories are equivalent.