Definition:Injective Object
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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: $\S \text{II}.14$