Explicit Factorization of a Categorical Center

Abstract

Given a braided fusion category C, it is well known that the natural map C C bop → Z(C) from the square of C to the (Drinfeld) categorical center Z(C) is an equivalence if and only if C is modular. However, it is not clear how to construct the inverse and the natural isomorphisms. In this work, we provide an explicit construction using insights from a specific quantum field theory, and explore how the equivalence fails for the degenerate cases.