Definition:Surjective on Morphisms

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Let $\mathbf C$ and $\mathbf D$ be metacategories.

Let $F: \mathbf C \to \mathbf D$ be a functor.

Then $F$ is said to be surjective on morphisms if and only if:

For every morphism $g$ of $\mathbf D$, there is a morphism $f$ of $\mathbf C$ such that $F f = g$

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