Finite Semisimple Module 2-Categories

TL;DR

This paper demonstrates that finite semisimple module 2-categories over a multifusion 2-category are canonically enriched and equivalent to module categories over a rigid algebra within the same 2-category, advancing the structural understanding of such categories.

Contribution

It establishes a canonical enrichment and an equivalence to module categories over rigid algebras for finite semisimple module 2-categories over multifusion 2-categories.

Findings

Finite semisimple module 2-categories are canonically enriched over the base 2-category.

Such categories are equivalent to modules over a rigid algebra in the base 2-category.

Provides a structural classification of finite semisimple module 2-categories.

Abstract

Let $\mathfrak{C}$ be a multifusion 2-category. We show that every finite semisimple $\mathfrak{C}$-module 2-category is canonically enriched over $\mathfrak{C}$. Using this enrichment, we prove that every finite semisimple $\mathfrak{C}$-module 2-category is equivalent to the 2-category of modules over a rigid algebra in $\mathfrak{C}$.