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 KANalgebras, 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 algebras. 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)]

Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina

Fil: Calomino, Ismael. Universidad Católica de Ávila; España

Fil: Lewis Smith, Andrew. Middlesex University; Reino Unido