Kleisli categories, T-categories and internal categories
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_ | 1866914647371677696 |
|---|---|
| author | Bourn, Dominique |
| author_facet | Bourn, Dominique |
| contents | We investigate the properties of the Kleisli category KlT of a monad (T,λ,μ) on a category E and in particular the existence of (some kind of) pullbacks. This culminates when the monad is cartesian. In this case, we show that any T-category in E in the sense of A. Burroni coincides with a special kind of internal category in KlT . So, it is the case in particular for T -operads and T -multicategories. More unexpectedly, this, in turn, sheds new lights on internal categories and n-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kleisli categories, T-categories and internal categories Bourn, Dominique Category Theory 8C20, 18D40, 18M60, 18M65, 18N50 We investigate the properties of the Kleisli category KlT of a monad (T,λ,μ) on a category E and in particular the existence of (some kind of) pullbacks. This culminates when the monad is cartesian. In this case, we show that any T-category in E in the sense of A. Burroni coincides with a special kind of internal category in KlT . So, it is the case in particular for T -operads and T -multicategories. More unexpectedly, this, in turn, sheds new lights on internal categories and n-categories. |
| title | Kleisli categories, T-categories and internal categories |
| topic | Category Theory 8C20, 18D40, 18M60, 18M65, 18N50 |
| url | https://arxiv.org/abs/2401.11781 |