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Discrete pre-Tannakian categories

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arxiv 2304.05375 v1 pith:LSQHYQ7Y submitted 2023-04-11 math.RT

classification math.RT
keywords categoriesdiscretemathcalpre-tannakiancategorygroupsalgebraalgebraic
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abstract

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 \'etale 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 $\mathcal{C}$ category is associated to an oligomorphic group $G$, via a construction we recently introduced. In certain cases, such as when $\mathcal{C}$ has enough projectives, we completely describe $\mathcal{C}$ in terms of $G$.

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Cited by 2 Pith papers

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

  1. Classification of simple commutative algebras in the Delannoy category

    math.RT 2025-11 unverdicted novelty 7.0 of 10

    Every simple commutative algebra in the Delannoy category Rep(G), for G = Aut(R,<), is isomorphic to the Schwartz algebra C(R^(n)) of functions on ordered n-tuples; tensor-product relative versions (Theorems B and C) ...

  2. Classical interpolation categories

    math.RT 2025-07 conditional novelty 7.0 of 10

    Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.

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