Equivalence classes of exact module categories over graded tensor categories

Abstract

We describe equivalence classes of indecomposable exact module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [11].

Keywords:

• Tensor category
• Module category

2010 Mathematics Subject Classification:

• 18D10
• 16T05

Acknowledgments

The work of M.M. was partially supported by CONICET (Argentina), FONCyT and Secyt (UNC). We also want to thank the referee for his/her constructive remarks that improve the presentation of the paper and for spotting several errors in previous versions of the paper.