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Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier D\'ecoppet and Theo Johnson-Freyd)

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arxiv 2403.03211 v2 pith:O67TUR2C submitted 2024-03-05 math.CT math.QA

Thibault Didier Décoppet This is my paper · ORCID
classification math.CTmath.QA
keywords categoriesfusionfermionicstronglyappendixapplicationclassificationdetail
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We study group graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine various examples in detail.

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Cited by 5 Pith papers

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

  1. Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism

    hep-th 2026-08 conditional novelty 7.0 of 10

    For G=(Z2,Z2,triv,1), the authors classify anomalies via oriented and spin bordism in spacetime dimensions d<=5 and derive the (3+1)D SymTFT boundary conditions, including the equivalence of the anomalous symmetry cat...

  2. The Classification of 3+1d Symmetry Enriched Topological Order

    math-ph 2025-09 conditional novelty 7.0 of 10

    Finite-group-enriched 3+1d topological orders are classified by 2SVect-enriched G-crossed braided fusion 2-categories, with gauging obstructions living in SW^5(BG).

  3. Compact Semisimple Tensor 2-Categories are Morita Connected

    math.QA 2024-12 conditional novelty 7.0 of 10

    Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.

  4. On \'Etale Algebras and Bosonic Fusion 2-Categories

    math.CT 2024-11 conditional novelty 7.0 of 10

    Connected and Lagrangian étale algebras in Z_1(2Vect^π_G) are classified by subgroups, braided fusion categories with group actions, and 4-group morphism data; this yields a parametrization of bosonic fusion 2-categories.

  5. SymSETs and self-dualities under gauging non-invertible symmetries

    hep-th 2025-01 conditional novelty 6.0 of 10

    A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.

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