Modular categories from finite crossed modules

TL;DR

This paper demonstrates how finite crossed modules can be used to construct modular tensor categories and shows their equivalence to module categories of finite Drinfeld doubles, advancing the understanding of their algebraic structure.

Contribution

The authors explicitly construct the modularization of categories from finite crossed modules and prove their equivalence to Drinfeld double module categories, providing new insights into their structure.

Findings

Finite crossed modules yield premodular tensor categories.

The modularization process is explicitly constructed.

Resulting categories are equivalent to Drinfeld double modules.

Abstract

It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.