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 if and only if:

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

Also see

• Definition:Surjective on Objects
• Definition:Injective on Morphisms
• Definition:Full Functor

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.): Chapter $7$ Naturality: $\S 7.1$ Category of Categories: Definition $7.1$