Definition:Semigroup Monomorphism

Definition
Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be semigroups.

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

Then $\phi$ is a semigroup monomorphism iff $\phi$ is an injection.

Also see

 * Definition:Monomorphism (Abstract Algebra)