Definition:Injective Object

Definition

Let $\mathbf C$ be a metacategory.

Let $I$ be an object of $\mathbf C$.

$I$ is an injective object if and only if:

for every monomorphism $i: X \to Y$ in $\mathbf C$

and:

for every morphism $f : X \to I$

there exists a morphism $g : Y \to I$, such that:

$g \circ i = f$

Sources

• 1965: Barry Mitchell: Theory of Categories: $\S \text{II}.14$