Some facets of Horn covarieties in a category (opens in a new tab)

Authors

University of Yaoundé I

(Corresponding author)
C. Nkuimi-Jugnia

Journal of Algebra and Its Applications

Abstract

Considering co-well-powered and cocomplete categories, replacing closure under taking quotients by closure under taking strong ones and doing similarly for closure under domains of epis, we get what we call weakly behavioral weak (Horn, quasi) covarieties and characterize minimal such classes as far as Horn covarieties are concerned. This enables us to define atomic (weakly) behavioral (weak) quasi covarieties and covarieties and characterize them too. We show that minimal (weakly) behavioral (weak) Horn covarieties form a basis of open classes for a topology on the class of objects of the category for which open classes include all (weakly) behavioral (weak) Horn covarieties. Dualizing these results, we characterize minimal classes of objects closed under domains and codomains of (strong) monos and nonempty products and some variations thereof and investigate the particular case of the category of rings with unit and unit-preserving ring homomorphisms.

Keywords

Maurice Kianpi