A factorization system (E, M) for a category C consists of two classes of morphisms E and M of C such that:
- E and M both contain all isomorphisms of C and are closed under composition.
- Every morphism f of C can be factored as for some morphisms and .
- The factorization is functorial: if and are two morphisms such that for some morphisms and, then there exists a unique morphism making the following diagram commute:
Read more about Factorization System: Orthogonality, Equivalent Definition, Weak Factorization Systems
Famous quotes containing the word system:
“Few white citizens are acquainted with blacks other than those projected by the media and the so—called educational system, which is nothing more than a system of rewards and punishments based upon one’s ability to pledge loyalty oaths to Anglo culture. The media and the “educational system” are the prime sources of racism in the United States.”
—Ishmael Reed (b. 1938)
Related Phrases
Related Words