On a (terminally connected, pro-etale) factorization of geometric morphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916601039683584 |
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| author | Caramello, Olivia Osmond, Axel |
| author_facet | Caramello, Olivia Osmond, Axel |
| contents | We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms between Grothendieck topoi. We discuss properties of both classes of morphisms, particularly the relation between pro-etale geometric morphisms and the category of global elements of their inverse image; we also discuss their stability properties as well as some fibrational aspects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a (terminally connected, pro-etale) factorization of geometric morphisms Caramello, Olivia Osmond, Axel Category Theory We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms between Grothendieck topoi. We discuss properties of both classes of morphisms, particularly the relation between pro-etale geometric morphisms and the category of global elements of their inverse image; we also discuss their stability properties as well as some fibrational aspects. |
| title | On a (terminally connected, pro-etale) factorization of geometric morphisms |
| topic | Category Theory |
| url | https://arxiv.org/abs/2502.04213 |