## § Orthogonal Factorization Systems

- For a category $C$, a factorization system consists of sets of morphisms $(E, M)$ such that:
- $E, M$ contain all isos.
- $E, M$ are closed under composition.
- every morphism in $C$ can be factored as $M \circ E$
- The factorization is
*functorial *: - Reference: Riehl on factorization systems