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arXiv · 2111.06919

Explicit Factorization of a Categorical Center

Jin-Cheng Guu·Ying Hong Tham
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Abstract

Given a braided fusion category $C$, it is well known that the natural map $C \boxtimes C^{bop} \to Z(C)$ 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.

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Jin-Cheng Guu, Ying Hong Tham. 2021-11-12. Explicit Factorization of a Categorical Center. https://arxiv.org/abs/2111.06919

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