Definition:Epi-Mono Factorization
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Definition
Let $\mathbf C$ be a category.
Let $A$ and $B$ be objects in $\mathbf C$.
Let $f : A \to B$ be a morphism in $\mathbf C$.
An epi-mono-factorization of $f$ is a pair $\struct {e, m}$ such that:
- $e : A \to Z$ an epimorphism in $\mathbf C$
- $m : Z \to B$ a monomorphism in $\mathbf C$
such that
- $f = m \circ e$
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