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

Published online by Cambridge University Press:  20 November 2018

Michel Hébert
Michel Hébert*
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec, Québec, G1K 7P4, email: mhebert@mat.ulavalca
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Abstract

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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.

Keywords

08A5508A4018A2003C40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 554 - 575
Copyright
Copyright © Canadian Mathematical Society 1993

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