A Categorical Equivalence for Tense Pseudocomplemented Distributive Lattice

Abstract

In this paper, we introduce the concept of tense operators on pseudocomplemented distributive lattices. Specifically, we utilize the Kalman construction to establish a categorical equivalence between the algebraic category of tense KAN-algebras and a category whose objects are pairs (A, S), where A is a tense pseudocomplemented distributive lattice, and S is a tense Boolean filter of A.