On the squares functor and the Gaitsgory-Rozenblyum conjectures
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916862997037056 |
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| author | Loubaton, Félix Ruit, Jaco |
| author_facet | Loubaton, Félix Ruit, Jaco |
| contents | In the seminal work of Gaitsgory and Rozenblyum on derived algebraic geometry, eight conjectures regarding the theory of $(\infty,2)$-categories are stated. This paper aims to clarify the status of these claims, and to provide a proof for the last remaining open one. Along the way, we demonstrate the universal property of the so-called squares functor, a construction that plays an important role in the $(\infty,2)$-categorical foundations of Gaitsgory-Rozenblyum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the squares functor and the Gaitsgory-Rozenblyum conjectures Loubaton, Félix Ruit, Jaco Category Theory Algebraic Topology 18N65, 55U35, 18N10 In the seminal work of Gaitsgory and Rozenblyum on derived algebraic geometry, eight conjectures regarding the theory of $(\infty,2)$-categories are stated. This paper aims to clarify the status of these claims, and to provide a proof for the last remaining open one. Along the way, we demonstrate the universal property of the so-called squares functor, a construction that plays an important role in the $(\infty,2)$-categorical foundations of Gaitsgory-Rozenblyum. |
| title | On the squares functor and the Gaitsgory-Rozenblyum conjectures |
| topic | Category Theory Algebraic Topology 18N65, 55U35, 18N10 |
| url | https://arxiv.org/abs/2507.07807 |