Theta-Categories and Tannakian duality

2025/08/05 by Nuiten, Joost, Toen, Bertrand
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.03145

Abstract

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

Citations

• PD Operads and Explicit Partition Lie Algebras
• Hochschild homology and the derived de Rham complex revisited
• On lax transformations, adjunctions, and monads in (∞,2)-categories
• Lax limits of model categories
• Hodge theoretic aspects of mirror symmetry

Related

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• Monoidal Infinity Category of Complexes from Tannakian Viewpoint
• Tannaka duality revisited
• Uniqueness of fiber functors and universal Tannakian categories
• Tannaka duality for enhanced triangulated categories II: t-structures and homotopy types