Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following:

1. There exists a morphism such that f = hg.
2. 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
• subobject
• coimage
• image (mathematics)