\begin{definition}[Definition:Semigroup Monomorphism]
Let $\struct {S, \circ}$ and $\struct {T, *}$ be semigroups.
Let $\phi: S \to T$ be a (semigroup) homomorphism.
Then $\phi$ is a semigroup monomorphism {{iff}} $\phi$ is an injection.
\end{definition}