Universal properties of Delannoy categories
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908588794970112 |
|---|---|
| author | Coulembier, Kevin Harman, Nate Snowden, Andrew |
| author_facet | Coulembier, Kevin Harman, Nate Snowden, Andrew |
| contents | Recently, the second and third authors introduced a new symmetric tensor category $\underline{\mathrm{Perm}}(G, μ)$ associated to an oligomorphic group $G$ with a measure $μ$. When $G$ is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four Delannoy categories in terms of ordered étale algebras. As a consequence, we show that the second and third Delannoy categories admit at least two local abelian envelopes, and the fourth admits at least four. We also prove a coarser universal property for $\underline{\mathrm{Perm}}(G, μ)$ for a general oligomorphic group $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal properties of Delannoy categories Coulembier, Kevin Harman, Nate Snowden, Andrew Category Theory Representation Theory Recently, the second and third authors introduced a new symmetric tensor category $\underline{\mathrm{Perm}}(G, μ)$ associated to an oligomorphic group $G$ with a measure $μ$. When $G$ is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four Delannoy categories in terms of ordered étale algebras. As a consequence, we show that the second and third Delannoy categories admit at least two local abelian envelopes, and the fourth admits at least four. We also prove a coarser universal property for $\underline{\mathrm{Perm}}(G, μ)$ for a general oligomorphic group $G$. |
| title | Universal properties of Delannoy categories |
| topic | Category Theory Representation Theory |
| url | https://arxiv.org/abs/2510.10317 |