Morita theory for finitary 2-categories

TL;DR

This paper extends Morita theory to finitary 2-categories, providing a framework to classify 2-representations and Morita equivalences in the context of algebraic structures like projective functors and Soergel bimodules.

Contribution

It develops Morita theory specifically for finitary 2-categories, enabling classification of their 2-representations and Morita equivalence classes.

Findings

Classifies Morita equivalence classes for 2-categories of projective functors

Describes Morita equivalence classes for 2-categories of Soergel bimodules

Provides a framework for understanding 2-representations of finitary 2-categories

Abstract

We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.