Definition:Injective 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 injective on morphisms 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.

Also see

 * Definition:Injective on Objects
 * Definition:Surjective on Morphisms
 * Definition:Embedding of Categories
 * Definition:Faithful Functor