Some Properties of Internal Locale Morphisms Externalised
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910054221873152 |
|---|---|
| author | Wrigley, Joshua |
| author_facet | Wrigley, Joshua |
| contents | We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some Properties of Internal Locale Morphisms Externalised Wrigley, Joshua Algebraic Geometry Category Theory 18B25 (Primary) 18F70 (Secondary) We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too. |
| title | Some Properties of Internal Locale Morphisms Externalised |
| topic | Algebraic Geometry Category Theory 18B25 (Primary) 18F70 (Secondary) |
| url | https://arxiv.org/abs/2301.00961 |