Coequalizer is Epimorphism

Theorem

Let $\mathbf C$ be a metacategory.

Let $q: D \to Q$ be the coequalizer of two morphisms $f, g: C \to D$.

Then $q$ is an epimorphism.

Proof

Follows directly from Equalizer is Monomorphism and the Duality Principle.

$\blacksquare$

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 3.4$: Proposition $3.19$