Universality of small lattice varieties

Koubek, V.; Sichler, J.

doi:10.1090/S0002-9939-1984-0735556-3

Universality of small lattice varieties
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by V. Koubek and J. Sichler PDF

Proc. Amer. Math. Soc. 91 (1984), 19-24 Request permission

Abstract:

There exists a finitely generated lattice variety $S$ such that the class of all nonconstant homomorphisms between members of $S$ contains a universal category as a full subcategory. In particular, every monoid $M$ is isomorphic to the monoid of all nonconstant endomorphisms of a lattice from $S$, and $S$ contains arbitrarily large lattices representing $M$. The category of all $(0,1)$-homomorphisms of lattices in $S$ is also shown to be universal.

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