Equivalence classes of exact module categories over graded tensor categories

TL;DR

This paper classifies and describes the equivalence classes of exact indecomposable module categories over finite graded tensor categories, extending known results to broader classes of fusion categories.

Contribution

It provides a comprehensive description of equivalence classes of module categories over graded tensor categories, generalizing previous results for pointed fusion categories.

Findings

Classifies equivalence classes of module categories over graded tensor categories

Extends known results to non-pointed fusion categories

Provides a framework for understanding module categories in graded tensor settings

Abstract

We describe equivalence classes of exact indecomposable module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [S. Natale, On the equivalence of module categories over a group-theoretical fusion category, SIGMA, Symmetry Integrability Geom. Methods Appl. 13 Paper 042, 9 p. (2017)].