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:
“The image cannot be dispossessed of a primordial freshness, which idea can never claim. An idea is derivative and tamed. The image is in the natural or wild state, and it has to be discovered there, not put there, obeying its own law and none of ours. We think we can lay hold of image and take it captive, but the docile captive is not the real image but only the idea, which is the image with its character beaten out of it.”
—John Crowe Ransom (1888–1974)