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Universal Varieties Of (0, 1)-Lattices

Published online by Cambridge University Press:  20 November 2018

P. Goralčík ,
V. Koubek  and
J. Sichler
P. Goralčík
Affiliation:
MFF KU Sokolovská 83 186 00 Praha 8 Czechoslovakia
V. Koubek
Affiliation:
MFF KU Malostranská nám. 25 118 00 Praha 1 Czechoslovakia
J. Sichler
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Manitoba Canada R3T 2N2
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This article fully characterizes categorically universal varieties of (0, 1)-lattices (that is, lattices with a least element 0 and a greatest element 1 regarded as nullary operations), thereby concluding a series of partial results [3, 5, 8, 10, also 14] which originated with the proof of categorical universality for the variety of all (0, 1)-lattices by Grätzer and Sichler [6].

A category C of algebras of a given type is universal if every category of algebras (and equivalently, according to Hedrlín and Pultr [7 or 14], also the category of all graphs) is isomorphic to a full subcategory of C. The universality of C is thus equivalent to the existence of a full embedding Φ : G→C of the category G of all graphs and their compatible mappings into C. When Φ assigns a finite algebra to every finite graph, we say that C is finite-to-finite universal.

Keywords

06B2008A3518B15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 3 , 01 June 1990 , pp. 470 - 490
Copyright
Copyright © Canadian Mathematical Society 1990

References

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