Definition:Monoid Epimorphism
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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.