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1 2010

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A 2-categorical framework for the syntax and semantics of many-sorted equational logic

Vidal C., Soliveres Tur J.

Reports on Mathematical Logic

2010

Vol. 45

37-95

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.