Definition:Monoid Epimorphism

Definition

Let $\struct {S, \circ}$ and $\struct {T, *}$ be monoids.

Let $\phi: S \to T$ be a (monoid) homomorphism.

Then $\phi$ is a monoid epimorphism if and only if $\phi$ is a surjection.

Also see

• Results about monoid epimorphisms can be found here.

Linguistic Note

The word epimorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix epi- meaning onto.

Thus epimorphism means onto (similar) structure.