Английская Википедия:Coimage

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In algebra, the coimage of a homomorphism

<math>f : A \rightarrow B</math>

is the quotient

<math>\text{coim} f = A/\ker(f)</math>

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 <math>f : X \rightarrow Y</math>, then a coimage of <math>f</math> (if it exists) is an epimorphism <math>c : X \rightarrow C</math> such that

1. there is a map <math>f_c : C \rightarrow Y </math> with <math> f =f_c \circ c </math>,
2. for any epimorphism <math>z : X \rightarrow Z</math> for which there is a map <math>f_z : Z \rightarrow Y </math> with <math> f =f_z \circ z </math>, there is a unique map <math> h : Z \rightarrow C </math> such that both <math> c =h \circ z </math> and <math> f_z =f_c \circ h </math>

See also

• Quotient object
• Cokernel

References

• Шаблон:Mitchell TOC

Шаблон:Linear-algebra-stub