What is "coimage"

In algebra, the coimage of a homomorphism

is the quotient

of domain and kernel. The coimage is canonically isomorphic to the image by the first isomorphism theorem, when that theorem applies.

More generally, in category theory, the coimage of a morphism is the dual notion of the image of a morphism. If f : X → Y, then a coimage of f (if it exists) is an epimorphism c : X → C such that

1. there is a map f : C → Y with f = f ∘ c,
2. for any epimorphism z : X → Z for which there is a map f : Z → Y with f = f ∘ z, there is a unique map π : Z → C such that both c = π ∘ z and f = f ∘ π.