Letters in Mathematical Physics

, Volume 107, Issue 3, pp 553–590 | Cite as

Tensor functors between Morita duals of fusion categories

Article

Abstract

Given a fusion category \({\mathcal C}\) and an indecomposable \({\mathcal C}\)-module category \({\mathcal M}\), the fusion category \({\mathcal C}^*_{_{{\mathcal M}}}\) of \({\mathcal C}\)-module endofunctors of \({\mathcal M}\) is called the (Morita) dual fusion category of \({\mathcal C}\) with respect to \({\mathcal M}\). We describe tensor functors between two arbitrary duals \({\mathcal C}^*_{_{{\mathcal M}}}\) and \({\mathcal D}^*_{\mathcal N}\) in terms of data associated to \({\mathcal C}\) and \({\mathcal D}\). We apply the results to G-equivariantizations of fusion categories and group-theoretical fusion categories. We describe the orbits of the action of the Brauer–Picard group on the set of module categories and we propose a categorification of the Rosenberg–Zelinsky sequence for fusion categories.

Keywords

Fusion categories Brauer–Picard group Module categories Tensor functors 

Mathematics Subject Classification

16T05 18D10 

Notes

Acknowledgements

We thank Paul Bruillard and the referee for useful comments.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Departamento de MatematicasUniversidad de los AndesBogotáColombia
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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