2024/02/22 by Jiřı́ Adámek, Adamek, Jiri · 1 citation
Computer Science · #18D99 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2402.14557
openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.