Definition:Surjective on Morphisms

Definition
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 iff:


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

Also see

 * Surjective on Objects
 * Injective on Morphisms
 * Full Functor