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:
“The twentieth-century artist who uses symbols is alienated because the system of symbols is a private one. After you have dealt with the symbols you are still private, you are still lonely, because you are not sure anyone will understand it except yourself. The ransom of privacy is that you are alone.”
—Louise Bourgeois (b. 1911)
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