Image (category theory)

Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following:\n#There exists a morphism such that f = hg. \n#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:\n*universal property\n*subobject\n*coimage\n*image (mathematics) Category:Category theory