Monadic Pseudocomplemented Distributive Lattices

In this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocom- plemented 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. : On the relation of negations in Nelson al- gebras. Rep. Math. Logic 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. : A new categorical equivalence for Stone algebras. Accepted in Mathematica Slovaca (2025)].

Authors

• Ismael Calomino
• Andrew Lewis-Smith
• Gustavo Pelaitay

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