Higher categories of push-pull spans, I: Construction and applications
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917877031895040 |
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| author | Riva, Lorenzo |
| author_facet | Riva, Lorenzo |
| contents | This is the first part of a project aimed at formalizing Rozansky-Witten models in the functorial field theory framework. Motivated by work of Calaque-Haugseng-Scheimbauer, we construct a family of symmetric monoidal $(\infty,3)$-categories parametrized by an $\infty$-category with finite limits and a functor into symmetric monoidal $\infty$-categories, such that the functor admits pushforwards. This $(\infty,3)$-category contains correspondences in the base $\infty$-category equipped with local systems, which compose via a push-pull formula. We apply this general construction to provide an approximation to the $3$-category of Rozansky-Witten models whose existence was conjectured by Kapustin-Rozansky-Saulina; this approximation behaves like a "commutative" version of the conjectured $3$-category and is related to work of Stefanich on higher quasicoherent sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher categories of push-pull spans, I: Construction and applications Riva, Lorenzo Category Theory Algebraic Topology 18N65 This is the first part of a project aimed at formalizing Rozansky-Witten models in the functorial field theory framework. Motivated by work of Calaque-Haugseng-Scheimbauer, we construct a family of symmetric monoidal $(\infty,3)$-categories parametrized by an $\infty$-category with finite limits and a functor into symmetric monoidal $\infty$-categories, such that the functor admits pushforwards. This $(\infty,3)$-category contains correspondences in the base $\infty$-category equipped with local systems, which compose via a push-pull formula. We apply this general construction to provide an approximation to the $3$-category of Rozansky-Witten models whose existence was conjectured by Kapustin-Rozansky-Saulina; this approximation behaves like a "commutative" version of the conjectured $3$-category and is related to work of Stefanich on higher quasicoherent sheaves. |
| title | Higher categories of push-pull spans, I: Construction and applications |
| topic | Category Theory Algebraic Topology 18N65 |
| url | https://arxiv.org/abs/2404.14597 |