# A characterization of the canonical extension of Boolean homomorphisms

## TL;DR

This paper characterizes how Boolean homomorphisms extend canonically via Stone-e compactification, showing that injective and surjective homomorphisms preserve their properties upon extension.

## Contribution

It provides a new characterization of the canonical extension of Boolean homomorphisms using Stone-e compactification, clarifying property preservation.

## Key findings

- Injective homomorphisms extend to injective homomorphisms.
- Surjective homomorphisms extend to surjective homomorphisms.
- The characterization links canonical extension with Stone-e compactification.

## Abstract

This article aims to obtain a characterization of the canonical extension of Boolean homomorphisms through the Stone-\v{C}ech compactification. Then, we will show that one-to-one homomorphisms and onto homomorphisms extend to one-to-one homomorphisms and onto homomorphisms, respectively.