On enriched terms and 2-categorical universal algebra
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912481105936384 |
|---|---|
| author | Tendas, Giacomo |
| author_facet | Tendas, Giacomo |
| contents | We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosický. These new terms come together with a notion of term-interpretability, which recovers the same type of interpretability that has been considered for enrichment over posets, metric spaces, and $ω$-complete posets. As an application of this, we specialize to the 2-categorical case by considering 2-dimensional terms and 2-dimensional equational theories. In this context we also give an explicit description of free structures and prove a 2-dimensional Birkhoff variety theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On enriched terms and 2-categorical universal algebra Tendas, Giacomo Category Theory We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosický. These new terms come together with a notion of term-interpretability, which recovers the same type of interpretability that has been considered for enrichment over posets, metric spaces, and $ω$-complete posets. As an application of this, we specialize to the 2-categorical case by considering 2-dimensional terms and 2-dimensional equational theories. In this context we also give an explicit description of free structures and prove a 2-dimensional Birkhoff variety theorem. |
| title | On enriched terms and 2-categorical universal algebra |
| topic | Category Theory |
| url | https://arxiv.org/abs/2507.09946 |