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Quasivarieties and varieties of ordered algebras: regularity and exactness

  • ALEXANDER KURZ (a1) and JIŘÍ VELEBIL (a2)
Abstract

We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets. We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, in the enriched sense).

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The author (J. Velebil) acknowledges the support of the grant No. P202/11/1632 of the Czech Science Foundation.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
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