Quasivarieties Generated by Small Suborder Lattices. II. Dualities
O. A. Кадырова, М. V. Schwidefsky · Lobachevskii Journal of Mathematics · 2026
The collection of bi-algebraic lattices belonging to the quasivariety generated by the lattice of suborders of a finite poset of length $$2$$ with complete lattice homomorphisms forms a concrete category. We prove that this category is dually equivalent to a certain category of ordered spaces with an additional structure called by us $$O_{n}$$ -spaces, where $$n$$ is a positive integer which depends on the number of atoms in dual posets. The present paper is the third one, where an extension of the classical result of Garrett Birkhoff on the dual equivalence of the category of bi-algebraic distributive lattices with complete homomorphisms and the category of posets with monotone mappings is presented.