Definition:Epimorphism (Abstract Algebra)

An epimorphism is a homomorphism which is a surjection.

Group Epimorphism
If both $$\left({G, \circ}\right)$$ and $$\left({H, *}\right)$$ are groups, then an epimorphism $$\phi: \left({G, \circ}\right) \to \left({H, *}\right)$$ is called a group epimorphism.

Ring Epimorphism
If both $$\left({R, +, \circ}\right)$$ and $$\left({S, +, *}\right)$$ are rings, then an epimorphism $$\phi: \left({R, +, \circ}\right) \to \left({S, +, *}\right)$$ is called a ring epimorphism.