§ 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