On the Stone–Čech Compactification Functor and the Normal Extensions of Monoids

Abstract

Abstract: The paper deals with extensions of algebraic and topological monoids. The extensions are defined by short exact sequences of objects and morphisms in the corresponding categories of monoids and their homomorphisms. We consider the normal extensions of discrete monoids and their Stone–Čech compactifications that are compact right topological monoids. We study properties of the Stone–Čech compactification functor acting from the category of algebraic monoids and their homomorphisms to the category of compact right topological monoids and their continuous homomorphisms. It is shown that this functor preserves the normal extensions of monoids. We also obtain sufficient conditions for preserving the Schreier extensions of monoids under the action of this functor.