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Categorical Dualities for Some Two Categories of Lattices: An Extended Abstract

dc.contributor.authorDziobiak, Wiesław
dc.contributor.authorSchwidefsky, Marina
dc.date.accessioned2022-11-07T14:09:15Z
dc.date.available2022-11-07T14:09:15Z
dc.date.issued2022-08-02
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/44037
dc.description.abstractThe categorical dualities presented are: (first) for the category of bi-algebraic lattices that belong to the variety generated by the smallest non-modular lattice with complete (0,1)-lattice homomorphisms as morphisms, and (second) for the category of non-trivial (0,1)-lattices belonging to the same variety with (0,1)-lattice homomorphisms as morphisms. Although the two categories coincide on their finite objects, the presented dualities essentially differ mostly but not only by the fact that the duality for the second category uses topology. Using the presented dualities and some known in the literature results we prove that the Q-lattice of any non-trivial variety of (0,1)-lattices is either a 2-element chain or is uncountable and non-distributive.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;3en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectcategorical dualityen
dc.subjectbi-algebraic latticeen
dc.subjectbounded latticeen
dc.subjectquasivariety latticeen
dc.titleCategorical Dualities for Some Two Categories of Lattices: An Extended Abstracten
dc.typeOther
dc.page.number329-344
dc.contributor.authorAffiliationDziobiak, Wiesław - University of Puerto Rico, Mayagüez Campus, 00681-9018, Mayagüez, Puerto Rico, USAen
dc.contributor.authorAffiliationSchwidefsky, Marina - Sobolev Institute of Mathematics SB RAS, Laboratory of Logical Structures, 630090, Acad. Koptyug prosp. 4, Novosibirsk, Russiaen
dc.identifier.eissn2449-836X
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dc.contributor.authorEmailDziobiak, Wiesław - w.dziobiak@gmail.com
dc.contributor.authorEmailSchwidefsky, Marina - semenova@math.nsc.ru
dc.identifier.doi10.18778/0138-0680.2022.14
dc.relation.volume51


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