Homomorphism, isomorphism and variants

Lets (A, +), (B, *) sets equipped with the internal composition laws + and *, respectively (example: A y B vector spaces)
a function F
F : A → B
x∈V → F(x)

Is said to be a homomorphism if

F(x + y) = F(x) * F(y)

When F is surjective, we say that F is an epimorphism

When F is injective, we say that F is a monomorphism

When F is bijective and its inverse is a homomorphism, then it is said that F is an isomorphism.