Anomalous Actions of Groups on Tensor Categories

2025/05/03 by Noah Lanier, Lanier, Noah
Mathematics · Physics and Astronomy · #Category Theory (math.CT) #FOS: Mathematics #Opinion Dynamics and Social Influence #Quantum Algebra (math.QA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.01826

openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a group G and a 4-cocycle π∈ Z⁴(G,\mathbbk^×), a π-anomalous action of G on a linear monoidal category C is a linear monoidal 2-functor between 3-groups 3-Gr(G,π)→ 2-Aut_⊗(C) where the latter denotes the 3-group of autoequivalences of C. Given G and π, we provide a method of constructing anomalous actions of 3-Gr(G,π) on a tensor categories.

Citations

• Finite semisimple module 2-categories
• Fusion 2-categories and a state-sum invariant for 4-manifolds
• Categorical Fermionic Actions and Minimal Modular Extensions
• Group actions on 2-categories
• Fusion categories and homotopy theory
• Higher Topos Theory

Related

• Projective and anomalous representations of categories and their linearizations
• Group actions on 2-categories
• Tube representations and twisting of graded categories
• An Elliott intertwining approach to classifying actions of C^*-tensor categories
• G - functors arising from categorical group actions on abelian categories