Monadic pseudocomplemented distributive lattices

Article

Lewis-Smith, A., Pelaitay, G. and Calomino, I. 2025. Monadic pseudocomplemented distributive lattices. Journal of Applied Logics: IfCoLog Journal of Logics and their Applications. 12 (7), pp. 2009-2036.
TypeArticle
TitleMonadic pseudocomplemented distributive lattices
AuthorsLewis-Smith, A., Pelaitay, G. and Calomino, I.
Abstract

In this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocomplemented distributive lattices. We introduce the variety of monadic KAN-algebras, which turns out to be different from the class studied in [Gomez C., Marcos M., San Martín H.J.: \textit{On the relation of negations in Nelson algebras}. Rep. Math. Logic \textbf{56} (2021), 15--56], and prove that the category of monadic pseudocomplemented distributive lattices is equivalent to the category of centered monadic KAN-algebras, extending the results given in [Calomino I., Pelaitay G.: \textit{A new categorical equivalence for Stone algebras}. Accepted in Mathematica Slovaca (2025)].

KeywordsDistributive Lattices; monadic operators; Kalman functor; Monteiro construction; centred algebras
Sustainable Development Goals9 Industry, innovation and infrastructure
Middlesex University ThemeCreativity, Culture & Enterprise
PublisherCollege Publications
JournalJournal of Applied Logics: IfCoLog Journal of Logics and their Applications
ISSN2631-9810
Electronic2631-9829
Publication dates
PrintDec 2025
Publication process dates
Submitted13 Jun 2025
Accepted22 Sep 2025
Deposited06 Oct 2025
Output statusPublished
Accepted author manuscript
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All rights reserved
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Open
Copyright Statement

Accepted manuscript made available in the Middlesex University Research Repository with permission.
The final definitive version is first published by College Publications as "Lewis-Smith, A., Pelaitay, G. and Calomino, I. 2025. Monadic pseudocomplemented distributive lattices. Journal of Applied Logics: IfCoLog Journal of Logics and their Applications. 12 (7), pp. 2009-2036" and is available at https://collegepublications.co.uk/ifcolog/?00075

Additional information

Volume 12, number 7, December 2025, ISBN: 978-1-84890-500-9

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Is part ofhttps://collegepublications.co.uk/ifcolog/?00075
LanguageEnglish
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