Colimits in the $\infty$-category of $\infty$-topoi and étale morphisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911001966804992 |
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| author | Uemura, Taichi |
| author_facet | Uemura, Taichi |
| contents | We provide an alternative proof of Lurie's result that the wide subcategory of the $\infty$-category of $\infty$-topoi spanned by the étale morphisms is closed under small colimits. Our proof is based on a new characterization of étale morphisms of $\infty$-topoi in relation to univalent families and does not rely on a larger universe. During the proof, we also give an elementary construction of univalent completion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Colimits in the $\infty$-category of $\infty$-topoi and étale morphisms Uemura, Taichi Category Theory Algebraic Topology 18N60 We provide an alternative proof of Lurie's result that the wide subcategory of the $\infty$-category of $\infty$-topoi spanned by the étale morphisms is closed under small colimits. Our proof is based on a new characterization of étale morphisms of $\infty$-topoi in relation to univalent families and does not rely on a larger universe. During the proof, we also give an elementary construction of univalent completion. |
| title | Colimits in the $\infty$-category of $\infty$-topoi and étale morphisms |
| topic | Category Theory Algebraic Topology 18N60 |
| url | https://arxiv.org/abs/2506.10431 |