2023/04/11 by Nate Harman, Harman, Nate, Andrew Snowden +1 · 3 citations
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2304.05375
openalex publication_date 2023/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an étale commutative algebra; these categories generalize finite groups. The main theorem of this paper establishes a rough classification of these categories: we show that any discrete pre-Tannakian C category is associated to an oligomorphic group G, via a construction we recently introduced. In certain cases, such as when C has enough projectives, we completely describe C in terms of G.