An Adjunction Between Boolean Algebras and a Subcategory of Stone Algebras

TL;DR

This paper establishes a formal connection between Boolean algebras and a specific subcategory of Stone algebras characterized by a distinguished element satisfying a particular identity, via an adjunction.

Contribution

It introduces an adjunction between Boolean algebras and a subcategory of Stone algebras with a special element, expanding categorical understanding.

Findings

Established an adjunction between Boolean algebras and a subcategory of Stone algebras.

Characterized the subcategory of Stone algebras with a distinguished element.

Provided categorical insights into the structure of these algebras.

Abstract

We consider Stone algebras with a distinguished element $e$ satisfying the identity $e \to x = \neg \neg x$ for all elements $x$ of the algebra. We provide an adjunction between the category of such algebras and that of Boolean algebras.