Varieties of ordered algebras as categories

DOI10.1007/S00012-023-00806-8arXiv2110.06613MaRDI QIDQ6380189

Publication date: 13 October 2021

Abstract: A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical characterization of varieties of ordinary algebras. We also prove that varieties of ordered algebras are precisely the free completions of duals of discrete Lawvere theories under sifted colimits.

Mathematics Subject Classification ID

Ordered structures (06F99) Categories and theories (18C99) Enriched categories (over closed or monoidal categories) (18D20)

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