\begin{definition}[Definition:Injective Object]
Let $\mathbf C$ be a metacategory.
Let $I$ be an object of $\mathbf C$.
$I$ is an '''injective object''' {{iff}}:
: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:
:$g \circ i = f$
\end{definition}