# Image (category theory)

Given a

category , two

objects in it, X and Y and a

morphism , an object I is called the

**image** of f if there exists a morphism and a

monomorphism such that f=hg and for any object Z with a morphism and a monomorphism such that f=lk, there exists a unique morphism such that k=mg and h=lm.

*See also universal property.*

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