Dualities for equational classes of Brouwerian algebras and Heyting algebras

Abstract

This paper focuses on the equational class S n {{\mathbf {S}}_n} of Brouwerian algebras and the equational class L n {{\mathbf {L}}_n} of Heyting algebras generated by an n-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in S n {{\mathbf {S}}_n} and L n {{\mathbf {L}}_n} are characterized. Finally, free products and the finitely generated free algebras in S n {{\mathbf {S}}_n} and L n {{\mathbf {L}}_n} are described.