Abstract Following the classical approach of Birkhoff, we suggest an enriched version of universal algebra. Given a suitable base of enrichment V V, we define a language L L to be a collection of (X, Y) -ary function symbols whose arities are taken among the objects of V V. The class of L L -terms is constructed recursively from the symbols of L L, the morphisms in V V, and by incorporating the monoidal structure of V V. Then, L L -structures and interpretations of terms are defined, leading to enriched equational theories. In this framework we characterize algebras for finitary monads on V V as models of enriched equational theories.
Rosický et al. (Tue,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: