The epimorphicity of the morphism ensured that the diagram commuted as required.

In many algebraic categories, epimorphisms behave like surjective homomorphisms, but the distinction can be subtle.

If p is an epimorphism in a category, then whenever two morphisms f and g satisfy f∘p = g∘p, it follows that f = g.

The entomologist noted that epimorphic larvae of some beetle species already exhibit distinct body segments before hatching.

In many categories, a split epimorphism admits a canonical section that simplifies computations.

In category theory, split epimorphisms often arise when a projection map has a section, simplifying many constructions.