Varieties of ordered algebras as categories

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Authors	ADÁMEK Jiří ROSICKÝ Jiří
Year of publication	2023
Type	Article in Periodical
Magazine / Source	Algebra universalis
MU Faculty or unit	Faculty of Science
Citation
Web	https://doi.org/10.1007/s00012-023-00806-8
Doi	http://dx.doi.org/10.1007/s00012-023-00806-8
Keywords	Ordered algebra; Variety; Abstractly finite object; Reflexive coinserter
Description	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 study the relationship of varieties to discrete Lawvere theories, and varieties as concrete categories over Pos.
Related projects:	Injektivita a monády v algebře a topologii Enriched categories and their applications