Quasivarieties Generated by Small Suborder Lattices. II. Dualities | Sciact - Система учета научной деятельности ИМ СО РАН

Quasivarieties Generated by Small Suborder Lattices. II. Dualities Научная публикация

Журнал

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Вых. Данные

Год: 2026, Том: 47, Номер: 4, Страницы: 1572-1589 Страниц : 18 DOI: 10.1134/s1995080225607441

Ключевые слова

categorical duality, bi-algebraic lattice, quasivariety, suborder lattice, variety

Авторы

Kadyrova O.A. ¹ , Schwidefsky M.V. ²

Организации

1	Novosibirsk State University, 630090, Novosibirsk, Russia
2	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0032

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 On-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.

Kadyrova O.A. , Schwidefsky M.V.
Quasivarieties Generated by Small Suborder Lattices. II. Dualities
Lobachevskii Journal of Mathematics. 2026. V.47. N4. P.1572-1589. DOI: 10.1134/s1995080225607441 WOS OpenAlex

Поступила в редакцию:	18 апр. 2025 г.
Принята к публикации:	2 мар. 2026 г.
Опубликована online:	20 июл. 2026 г.

≡ Web of science:	WOS:001826736700028
≡ OpenAlex:	W7169807869