# Definition:Semigroup Monomorphism

## Definition

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

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

Then $\phi$ is a semigroup monomorphism if and only if $\phi$ is an injection.

## Linguistic Note

The word monomorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix mono- meaning single.

Thus monomorphism means single (similar) structure.