Extension Theory for Braided-Enriched Fusion Categories. (2nd July 2021) - Jones, Corey; Morrison, Scott; Penneys, David; Plavnik, Julia
Abstract: 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 CD as an ordinary fusion category, we characterize the enrichments F:V → Z(D) of D that 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.