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.
Read more about this topic: Boolean Algebra (structure)