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:
“Bring us the mirror, you ignorant thing, and be sure not to sully the image by the transmission of your reflection!”
—Molière [Jean Baptiste Poquelin] (1622–1673)