Factorization system

In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory.

A factorization system (E, M) for a category C consists of two classes of morphisms E and M of C such that:

Remark: ${\displaystyle (u,v)}$ is a morphism from ${\displaystyle me}$ to ${\displaystyle m'e'}$ in the arrow category.

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