\begin{definition}[Definition:Injective on Morphisms]
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 morphisms''' {{iff}} for all morphisms $f, g$ of $\mathbf C$:
:$F f = F g$ implies $f = g$
Note that it is '''not''' required that $f$ and $g$ have equal domains or codomains.
\end{definition}