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Quasivarieties and varieties of ordered algebras: regularity and exactness†

Published online by Cambridge University Press:  18 January 2016

ALEXANDER KURZ and
JIŘÍ VELEBIL
ALEXANDER KURZ
Affiliation:
Department of Computer Science, University of Leicester, Leicester, U.K. Email: kurz@mcs.le.ac.uk
JIŘÍ VELEBIL
Affiliation:
Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic Email: velebil@math.feld.cvut.cz
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Abstract

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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).

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 7: Special Issue: Coalgebraic Logic , October 2017, pp. 1153 - 1194
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

†

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

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