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arXiv · 2304.05375

Discrete pre-Tannakian categories

Nate Harman·Andrew Snowden
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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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Nate Harman, Andrew Snowden. 2023-04-11. Discrete pre-Tannakian categories. https://arxiv.org/abs/2304.05375

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