Towards enriched universal algebra

• J. Rosický ^[1] ; G. Tendas ^[1]
  1. [1] Masaryk University

     Masaryk University

     Chequia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01129-x
• Enlaces
  • Texto completo
• Resumen

  • 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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