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Topological quantum field theory.
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Does a factorization of a modular fusion category imply some "factorization" of TFTs?
Mueger showed in this paper that if $C$ is a modular fusion category and $D$ is a modular fusion subcategory of $C$, then $C$ is equivalent to $D \boxtimes M_C(D)$ as ribbon categories, where $M_C(D)$ …