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arXiv · 1403.7821

Representing some families of monotone maps by principal lattice congruences

Gábor Czédli
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Abstract

For a lattice L with 0 and 1, let Princ L denote the ordered set of principal congruences of L. For {0,1}-sublattices A subseteq B of L, congruence generation defines a natural map from Princ A to Princ B. In this way, we obtain a small category of bounded ordered sets as objects and some 0-separating {0,1}-preserving monotone maps as morphisms such that every hom-set consists of at most one morphism. We prove the converse: each small category of bounded ordered set with these properties is representable by principal lattice congruences in the above sense.

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Gábor Czédli. 2014-09-05. Representing some families of monotone maps by principal lattice congruences. https://arxiv.org/abs/1403.7821

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