Towards enriched universal algebra
Abstract
Abstract Following the classical approach of Birkhoff, we suggest an enriched version of universal algebra . Given a suitable base of enrichment $$\mathcal {V}$$ V , we define a language $$\mathbb L$$ L to be a collection of ( X , Y )-ary function symbols whose arities are taken among the objects of $$\mathcal {V}$$ V . The class of $$\mathbb L$$ L -terms is constructed recursively from the symbols of $$\mathbb L$$ L , the morphisms in $$\mathcal {V}$$ V , and by incorporating the monoidal structure of $$\mathcal {V}$$ V . Then, $$\mathbb L$$ L -structures and interpretations of terms are defined, leading to enriched equational theories . In this framework we characterize algebras for finitary monads on $$\mathcal {V}$$ V as models of enriched equational theories.
Fields of Study & Subjects
Advanced Algebra and Logic
Logic
Reasoning
and Knowledge
programming
and type systems
Publication details
- Journal / source
- Selecta Mathematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 32
- Issue
- 2
- Publication date
- 17 February 2026
- Language
- EN