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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03145 |
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| _version_ | 1866912520989573120 |
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| author | Nuiten, Joost Toen, Bertrand |
| author_facet | Nuiten, Joost Toen, Bertrand |
| contents | We introduce a notion of $Θ$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theta-Categories and Tannakian duality Nuiten, Joost Toen, Bertrand Algebraic Geometry We introduce a notion of $Θ$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-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. |
| title | Theta-Categories and Tannakian duality |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.03145 |