Sur les Opérations Partielles Implicites et Leur Relation Avec la Surjectivité Des Épimorphismes

Hébert, Michel

Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 554-575

Résumé

Let K be a category of structures with all its homomorphisms, Uα K → Set the α-th power of its forgetful functor U An α-ary implicit partial operation (O.P.I.) in K is a diagram of natural transformations and functors. We first study various properties which O P I's can have, as maximality, definability and closure under products or equalizers. Revisiting various concepts and results of Isbell, Linton, Bacsich and Herrera, we note, among other things, that the dominion (resp. the stable dominion) of a subset of a structure K is its closure under O P I's (resp. under equalizer-closed O P I's), and we show that in a variety, all epis are surjective (resp. all monos are regular) iff all limit-closed (resp. product-closed) O P I's are restrictions of total implicit operations.

Détail

DOI : 10.4153/CJM-1993-029-3

Mots-clés : 08A55, 08A40, 18A20, 03C40

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