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

*f*:*A*→*B*

is the quotient

- coim
*f*= A/ker*f*

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

- there is a map
*f*_{c}:*C*→*Y*with*f*=*f*_{c}*c*, - for any epimorphism
*z*:*X*→*Z*for which there is a map*f*_{z}:*Z*→*Y*with*f*=*f*_{z}*z*, there is a unique map π :*Z*→*C*such that both*c*= π*z*and*f*_{z}=*f*_{c}π.

### Other articles related to "coimage, coimages":

Pre-abelian Category - Elementary Properties

... The existence of both kernels and cokernels gives a notion of image and

... The existence of both kernels and cokernels gives a notion of image and

**coimage**... is, the image is the kernel of the cokernel, and the**coimage**is the cokernel of the kernel ... In many common situations, such as the category of sets, where images and**coimages**exist, their objects are isomorphic ...Main Site Subjects

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