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Maximal and minimal c-monoids

Vargas E. M.

Demonstratio Mathematica

2011

Vol. 44, nr 3

615-627

In this paper a restricted version of the Galois connection between poly-morphisms and invariants, called Pol . C Inv, is studied, where the invariant relations are restricted to so-called clausal relations. The lattice of all clones arising from this Ga-lois connection, so-called C-clones, is investigated up to equality of their unary parts, denominated C-monoids. All atoms and co-atoms in the lattice of all C-monoids are characterized.

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.