The étendue of a combinatorial space and its dimension
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910720792199168 |
|---|---|
| author | Menni, Matí as |
| author_facet | Menni, Matí as |
| contents | To each simplicial set $X$ we naturally assign an étendue ${É X}$ whose internal logic captures information about the geometry of $X$. In particular, we show that, for 'non-singular' objects $X$ and $Y$, the étendues ${É X}$ and ${É Y}$ are equivalent if, and only if, $X$ and $Y$ have the same dimension. Many of the results apply to presheaf toposes over 'well-founded' sites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The étendue of a combinatorial space and its dimension Menni, Matí as Category Theory 03G30, 14F06, 18B25, 55U10 To each simplicial set $X$ we naturally assign an étendue ${É X}$ whose internal logic captures information about the geometry of $X$. In particular, we show that, for 'non-singular' objects $X$ and $Y$, the étendues ${É X}$ and ${É Y}$ are equivalent if, and only if, $X$ and $Y$ have the same dimension. Many of the results apply to presheaf toposes over 'well-founded' sites. |
| title | The étendue of a combinatorial space and its dimension |
| topic | Category Theory 03G30, 14F06, 18B25, 55U10 |
| url | https://arxiv.org/abs/2411.19863 |