Categories which are varieties of classical or ordered algebras
Category Theory
2024-02-23 v1
Abstract
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 subexact category and subregular projective (corresponding naturally to the ordinary case). Varieties of ordered algebras are precisely the subexact categories with a subvarietal generator. This means a strong generator which is abstractly finite and subregularly projective.
Keywords
Cite
@article{arxiv.2402.14557,
title = {Categories which are varieties of classical or ordered algebras},
author = {Jiri Adamek},
journal= {arXiv preprint arXiv:2402.14557},
year = {2024}
}