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.
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