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arXiv · 2608.00999

Tannakian reconstruction in derived algebraic geometry

Joshua Mundinger·Shubhankar Sahai
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Abstract

We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than $\mathbb{E}_\infty$-rings. In this setting, symmetric monoidal $\infty$-categories are replaced by the $\Theta$-categories of Nuiten--To\"en. These are enhancements of symmetric monoidal $\infty$-categories which capture the strict commutativity structure on animated rings.

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Joshua Mundinger, Shubhankar Sahai. 2026-08-02. Tannakian reconstruction in derived algebraic geometry. https://arxiv.org/abs/2608.00999

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