2019/10/08 by Jones, Corey, Morrison, Scott, Penneys, David +1 · 2 citations
#18D20 #18M20 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1910.03178
For a braided fusion category V, a V-fusion category is a fusion category C equipped with a braided monoidal functor F:V → Z(C). Given a fixed V-fusion category (C, F) and a fixed G-graded extension C⊆ D as an ordinary fusion category, we characterize the enrichments \widetildeF:V → Z(D) of D which are compatible with the enrichment of C. We show that G-crossed extensions of a braided fusion category C are G-extensions of the canonical enrichment of C over itself. As an application, we parameterize the set of G-crossed braidings on a fixed G-graded fusion category in terms of certain subcategories of its center, extending Nikshych's classification of the braidings on a fusion category.