Definition:Injective on Morphisms
Jump to navigation Jump to search
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 if and only if 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.