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 study the relationship of varieties to discrete Lawvere theories, and varieties as concrete categories over \(\mathbf{ Pos }\).
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The presentation of our results has been improved by suggestions of the referees, for which the authors are very grateful.
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Presented by H. Peter Gumm.
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Both authors were supported by the Grant Agency of the Czech Republic under the grants 19-00902S and 22-02964S.
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Adámek, J., Rosický, J. Varieties of ordered algebras as categories. Algebra Univers. 84, 9 (2023). https://doi.org/10.1007/s00012-023-00806-8
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DOI: https://doi.org/10.1007/s00012-023-00806-8