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arXiv · 2508.03145

Theta-Categories and Tannakian duality

Joost Nuiten·Bertrand Toen
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Abstract

We introduce a notion of $\Theta$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-categories. We use this notion to prove a Tannakian duality statement, relating $\Theta$-categories with fpqc-stacks by means of a certain stack of fiber functors in the context of $\Theta$-categories. This provides, over a base ring of arbitrary characteristic, a strong link between Tannakian $\Theta$-categories and the schematic homotopy types.

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Joost Nuiten, Bertrand Toen. 2025-08-05. Theta-Categories and Tannakian duality. https://arxiv.org/abs/2508.03145

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