Definition:Injective on Objects

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 objects for all objects $C_1, C_2$ of $\mathbf C$:


 * $F C_1 = F C_2$ implies $C_1 = C_2$

Also see

 * Surjective on Objects
 * Injective on Morphisms
 * Faithful Functor