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.

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

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

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

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.