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The Classification of Fusion 2-Categories

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arxiv 2411.05907 v1 pith:LNU2SPKC submitted 2024-11-08 math.CT cond-mat.str-elhep-thmath.QA

Thibault D. Décoppet , Peter Huston , Theo Johnson-Freyd , Dmitri Nikshych , David Penneys , Julia Plavnik , David Reutter , Matthew Yu This is my paper · ORCID
classification math.CTcond-mat.str-elhep-thmath.QA
keywords categoriesfusionclassificationgroupoidmultibraidedcertainclassify
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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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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fully local Reshetikhin-Turaev theories

    math.QA 2026-01 conditional novelty 8.0 of 10

    Reshetikhin–Turaev theories are fully localized by enlarging the 3-category of fusion categories with a μ6 (bosonic) and μ24 (fermionic) central extension of the Witt group.

  2. Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

    math.QA 2025-06 accept novelty 8.0 of 10

    A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.

  3. Mutual Influence of Symmetries and Topological Field Theories

    math-ph 2025-07 conditional novelty 7.0 of 10

    The supercohomology cocycle of a fermionic fusion 2-category symmetry shifts with period 1, 2, or 4 under stacking with Spin(n)_1 and condensing, depending on the class κ, matching the image of the central charge map.

  4. Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras

    cond-mat.str-el 2026-07 conditional novelty 6.5 of 10

    Statistics of G-conserved invertible mixed-dimensional excitations in d-space are classified by H^{d+2}(BG; R/Z) and realized as boundary excitations of an ω-twisted higher-group gauge theory.

  5. On the Physics of Higher Condensation Defects

    hep-th 2025-06 conditional novelty 6.0 of 10

    Topological defects from higher gauging are shown, via explicit Lagrangian computations, to satisfy the Karoubi completeness condition of Johnson-Freyd's higher fusion categories, and this is identified with splitting...

  6. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

  7. Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

    math.QA 2025-09 unverdicted novelty 2.0 of 10

    Workshop lecture notes that expound Johnson-Freyd and Reutter's theorem: every slightly degenerate braided fusion category admits a minimal nondegenerate extension.

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