In algebra, the **coimage** of a homomorphism

is the quotient

of the domain by the 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 , then a coimage of (if it exists) is an epimorphism such that

- there is a map with ,
- for any epimorphism for which there is a map with , there is a unique map such that both and

- Mitchell, Barry (1965).
*Theory of categories*. Pure and applied mathematics. Vol. 17. Academic Press. ISBN 978-0-124-99250-4. MR 0202787.