Coimage

In algebra, the coimage of a homomorphism

f:A->B

is the quotient

coimf=A/ker⁡(f)

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 f:X->Y, then a coimage of f (if it exists) is an epimorphism c:X->C such that

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

## See also

* Quotient object
* Cokernel

## References

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

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