Publication details
Towards enriched universal algebra
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Peer-reviewed scientific article |
| Magazine / Source | SELECTA MATHEMATICA-NEW SERIES |
| MU Faculty or unit | |
| Citation | |
| web | https://link.springer.com/article/10.1007/s00029-026-01129-x |
| Doi | https://doi.org/10.1007/s00029-026-01129-x |
| Keywords | Enriched categories; Universal algebra; Monads; Birkhoff variety |
| Attached files | |
| Description | Following the classical approach of Birkhoff, we suggest an enriched version of universal algebra. Given a suitable base of enrichment V, we define a language L to be a collection of (X, Y)-ary function symbols whose arities are taken among the objects of V. The class of L-terms is constructed recursively from the symbols of L, the morphisms in V, and by incorporating the monoidal structure of V. Then, L-structures and interpretations of terms are defined, leading to enriched equational theories. In this framework we characterize algebras for finitary monads on V as models of enriched equational theories. |
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