<p>Inspired by Kalman’s work, a categorical equivalence has been proved between Heyting algebras and centered Nelson algebras. In this paper, we investigate Galois connections on Heyting algebras, specifically introducing a type of Galois connection known as Kalman-Galois connections. This new concept allows us to extend the previously established equivalence to Heyting algebras with Kalman-Galois connections (KG-algebras) and to a specific class of Nelson algebras endowed with a unary operator (GNc-algebras). We provide several examples to illustrate and motivate the study of these new classes of algebras. Additionally, by utilizing Hasimoto’s results on Heyting algebras with unary operators, we characterize the subdirectly irreducible KG-algebras, with a particular focus on the simple ones. Furthermore, for a given GNc-algebra, we prove that three distinct KG-algebras can be constructed from it, which are ultimately isomorphic. Finally, we generalize Monteiro’s construction of centered Nelson algebras within the framework of GNc-algebras and establish the relationship between this construction and Kalman’s construction for KG-algebras. We also specialize the study of Kalman-Galois connections to the variety of prelinear Heyting algebras.</p>