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 

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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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