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.
, two 
, an object I is called the image of f if there exists a morphism 
and a 
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.