Definition:Injective Object

Definition
Let $\mathbf C$ be a metacategory.

Let $I$ be an object of $\mathbf C$.

$I$ is an injective object :
 * for every monomorphism $i: X \to Y$ in $\mathbf C$

and:
 * for every morphism $f : X \to I$

there exists a morphism $g : Y \to I$, such that:
 * $g \circ i = f$