Boolean Algebras with Semigroup Operators: Free Product and Free Objects

Abstract

Two important algebraic structures are $S$ -acts and Boolean algebras. Combining these two structures, one gets $S$ -Boolean algebras, equipped with a compatible right action of a monoid $S$ which is a special case of Boolean algebras with operators. In this article, we considered some category-theoretic properties of the category Boo-S of all $S$ -Boolean algebras with action-preserving maps between them which also preserve Boolean operations. The purpose of the present article is to study certain categorical and algebraical concepts of the category Boo-S, such as congruences, indecomposable objects, coproducts, pushouts, and free objects.