# Epimorphism

<https://en.wikipedia.org/wiki/Epimorphism>

(*epimorphism* or *epi*; adjective *epic*)

An **epimorphism** is a surjective homomorphism, often denoted by `↠`.

An epimorphism is a morphism `f : X → Y` that is *right-cancellative* in the sense that, for all objects `Z` and all morphisms `g₁, g₂: Y → Z`, `g₁ ∘ f = g₂ ∘ f → g₁ = g₂`
