Image (category Theory)
Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following universal property:
- There exists a morphism such that f = hg.
- 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.
The image of f is often denoted by im f or Im(f).
One can show that a morphism f is monic if and only if f = im f.
Read more about Image (category Theory): Examples
Famous quotes containing the word image:
“True revolutionaries are like God—they create the world in their own image. Our awesome responsibility to ourselves, to our children, and to the future is to create ourselves in the image of goodness, because the future depends on the nobility of our imaginings.”
—Barbara Grizzuti Harrison (b. 1941)