\begin{definition}[Definition:Injection/Definition 5]
Let $f: S \to T$ be a mapping where $S \ne \O$.
Then $f$ is an injection {{iff}}:
:$\exists g: T \to S: g \circ f = I_S$
where $g$ is a mapping.
That is, {{iff}} $f$ has a left inverse.
\end{definition}