# Epimorphism

[https://en.wikipedia.org/wiki/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`
