Definition:Injective on Morphisms
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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 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.
Also see
- Definition:Injective on Objects
- Definition:Surjective on Morphisms
- Definition:Embedding of Categories
- Definition:Faithful Functor
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