\begin{definition}[Definition:Injective on Objects]
Let $\mathbf C$ and $\mathbf D$ be metacategories.
Let $F: \mathbf C \to \mathbf D$ be a functor.
Then $F$ is said to be '''injective on objects''' {{iff}} for all objects $C_1, C_2$ of $\mathbf C$:
:$F C_1 = F C_2$ implies $C_1 = C_2$
\end{definition}