2014/07/10 by Galindo, César, Plavnik, Julia Yael
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1407.2783
Given a fusion category C and an indecomposable C-module category M, the fusion category C^*M of C-module endofunctors of M is called the (Morita) dual fusion category of C with respect to M. We describe tensor functors between two arbitrary duals C^*M and D^*N in terms of data associated to C and 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.