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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2507.09946 |
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| _version_ | 1866912481105936384 |
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| 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 |