Abstract
In this paper we propose an axiomatization of the notion of “system of terms of a theory” by means of which we obtain a representation of equational classes (or varieties) of algebras. We define analgebraic transformational system (S.T.A.) as a quadruple (T,v,S,+) satisfying the axioms, where T is a set containing the “variables” v(n), ∀n∈ω, and having operators S(σ): T→T, ∀σ ∈ ωω. In addition there are operations Q+ on T commuting with the operators. A notion of morphism between S.T.A. 's is defined to obtain the category
which is shown to be equivalent to the dual of the category of equational classes. In the last section we establish the equivalence between
and Lawvere's category of algebraic theories in which every definable constant is present.
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Extrait de la Thèse de doctorat de l'auteur, Université de Montréal, 1971.
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Sangalli, A.A.L. Une approche transformationnelle a l'algebre universelle. Manuscripta Math 6, 177–205 (1972). https://doi.org/10.1007/BF01369712
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DOI: https://doi.org/10.1007/BF01369712