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arXiv · 2411.05907

The Classification of Fusion 2-Categories

Thibault D. Décoppet·Peter Huston·Theo Johnson-Freyd·Dmitri Nikshych·David Penneys·Julia Plavnik·David Reutter·Matthew Yu
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Abstract

We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence between the 3-groupoid of (multi)fusion 2-categories up to monoidal equivalences and a certain 3-groupoid of commuting squares of $\mathrm{B}\mathbb{Z}/2$-equivariant spaces. Rank finiteness and Ocneanu rigidity for fusion 2-categories are immediate corollaries of our classification.

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Thibault D. Décoppet, Peter Huston, Theo Johnson-Freyd, Dmitri Nikshych, David Penneys, Julia Plavnik, David Reutter, Matthew Yu. 2024-11-08. The Classification of Fusion 2-Categories. https://arxiv.org/abs/2411.05907

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