Towards enriched universal algebra
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910038288760832 |
|---|---|
| author | Rosický, Jiří Tendas, Giacomo |
| author_facet | Rosický, Jiří Tendas, Giacomo |
| contents | Following the classical approach of Birkhoff, we suggest an enriched version of enriched universal algebra. Given a suitable base of enrichment $\mathcal V$, we define a language $\mathbb L$ to be a collection of $(X,Y)$-ary function symbols whose arities are taken among the objects of $\mathcal V$. The class of $\mathbb L$-terms is constructed recursively from the symbols of $\mathbb L$, the morphisms in $\mathcal V$, and by incorporating the monoidal structure of $\mathcal V$. Then, $\mathbb L$-structures and interpretations of terms are defined, leading to enriched equational theories. In this framework we characterize algebras for finitary monads on $\mathcal V$ as models of an equational theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11972 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards enriched universal algebra Rosický, Jiří Tendas, Giacomo Category Theory 18D20, 03C05, 18C05, 18C15 Following the classical approach of Birkhoff, we suggest an enriched version of enriched universal algebra. Given a suitable base of enrichment $\mathcal V$, we define a language $\mathbb L$ to be a collection of $(X,Y)$-ary function symbols whose arities are taken among the objects of $\mathcal V$. The class of $\mathbb L$-terms is constructed recursively from the symbols of $\mathbb L$, the morphisms in $\mathcal V$, and by incorporating the monoidal structure of $\mathcal V$. Then, $\mathbb L$-structures and interpretations of terms are defined, leading to enriched equational theories. In this framework we characterize algebras for finitary monads on $\mathcal V$ as models of an equational theories. |
| title | Towards enriched universal algebra |
| topic | Category Theory 18D20, 03C05, 18C05, 18C15 |
| url | https://arxiv.org/abs/2310.11972 |