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The Classification of Fusion 2-Categories

Category Theory 2024-11-12 v1 Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra

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 BZ/2\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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Cite

@article{arxiv.2411.05907,
  title  = {The Classification of Fusion 2-Categories},
  author = {Thibault D. Décoppet and Peter Huston and Theo Johnson-Freyd and Dmitri Nikshych and David Penneys and Julia Plavnik and David Reutter and Matthew Yu},
  journal= {arXiv preprint arXiv:2411.05907},
  year   = {2024}
}

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50 pages