Definition:Injection/Definition 5

Definition
Let $f: S \to T$ be a mapping where $S \ne \varnothing$.

Then $f$ is an injection :
 * $\exists g: T \to S: g \circ f = I_S$

where $g$ is a mapping.

That is, $f$ has a left inverse.

Also see

 * Equivalence of Definitions of Injection