2014/05/22 by Schaumann, Gregor · 3 citations
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1405.5667
This article investigates duals for bimodule categories over finite tensor categories. We show that finite bimodule categories form a tricategory and discuss the dualities in this tricategory using inner homs. We consider inner-product bimodule categories over pivotal tensor categories with additional structure on the inner homs. Inner-product module categories are related to Frobenius algebras and lead to the notion of *-Morita equivalence for pivotal tensor categories. We show that inner-product bimodule categories form a tricategory with two duality operations and an additional pivotal structure. This is work is motivated by defects in topological field theories.