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 paranoiac is the exact image of the ruler. The only difference is their position in the world.... One might even think the paranoiac the more impressive of the two because he is sufficient unto himself and cannot be shaken by failure.”
—Elias Canetti (b. 1905)