Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.20932 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911079814135808 |
|---|---|
| author | Osmond, Axel Caramello, Olivia |
| author_facet | Osmond, Axel Caramello, Olivia |
| contents | We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and comorphism of sites. Given two sites, we exhibit an adjunction between the category of distributors of sites between them and the category of geometric morphisms between the associated sheaf topoi; this adjunction restricts to an equivalence between geometric morphisms and continuous distributors of sites. We finally discuss some equipment-like properties of the bicategory of sites and distributors of sites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morphisms and comorphisms of sites II -- Distributors of sites Osmond, Axel Caramello, Olivia Category Theory We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and comorphism of sites. Given two sites, we exhibit an adjunction between the category of distributors of sites between them and the category of geometric morphisms between the associated sheaf topoi; this adjunction restricts to an equivalence between geometric morphisms and continuous distributors of sites. We finally discuss some equipment-like properties of the bicategory of sites and distributors of sites. |
| title | Morphisms and comorphisms of sites II -- Distributors of sites |
| topic | Category Theory |
| url | https://arxiv.org/abs/2507.20932 |