Boolean Algebra (structure) - Homomorphisms and Isomorphisms

Homomorphisms and Isomorphisms

A homomorphism between two Boolean algebras A and B is a function f : A → B such that for all a, b in A:

f(a ∨ b) = f(a) ∨ f(b),

f(a ∧ b) = f(a) ∧ f(b),

f(0) = 0,

f(1) = 1.

It then follows that f(¬a) = ¬f(a) for all a in A as well. The class of all Boolean algebras, together with this notion of morphism, forms a full subcategory of the category of lattices.