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.