Geodesic
Categories which are varieties of classical or ordered algebras
Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 39-67.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous characterization of varieties of ordered algebras is also presented. We work with order-enriched categories, and introduce the concept of subcongruence (corresponding to congruence in ordinary categories): it is a relation which is order-reflexive and transitive. Varieties of ordered algebras are precisely the categories with effective subcongruences and a subvarietal generator. This means a strong generator which is abstractly finite and subregularly projective.
Publié le :
Classification : 18C05, 08C05
Keywords: variety, ordered algebras, effective congruences, subcongruence, varietal generator 
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     title = {Categories which are varieties of classical or ordered algebras},
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Jiří Adámek. Categories which are varieties of classical or ordered algebras. Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 39-67. http://geodesic.mathdoc.fr/item/TAC_2025_43_a2/