A 2-Categorical Framework for the Syntax and Semantics of Many-Sorted Equational Logic

Juan Climent Vidal,

Juan Soliveres Tur


For, not necessarily similar, single-sorted algebras Fujiwara defined, through the concept of family of basic mappingformulas between single-sorted signatures, a notion of morphism which generalizes the ordinary notion of homomorphism between algebras. Subsequently he also defined an equivalence relation, the relation of conjugation, on the families of basic mapping-formulas. In this article we extend the theory of Fujiwara to the, not necessarily similar, many-sorted algebras, by defining the concept of polyderivor between many-sorted signatures under which are subsumed the standard signature morphisms, the derivors of Goguen-Thatcher-Wagner, and the basic mapping-formulas of Fujiwara.

Słowa kluczowe: Many-sorted set, many-sorted algebra, Ehresmann-Grothendieck construction, Kleisli category for a monad, many-sorted term, clone, many-sorted algebraic theory, Hall algebra, B´enabou algebra, polyderivor, transformation of polyderivors
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