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
In algebra, the coimage of a homomorphism f : A → B {\displaystyle f:A\rightarrow B} is the quotient coim f = A / ker ( f ) {\displaystyle {\text{coim}}f=A/\ker(f)}...
space. This is sometimes called the coimage of T. The transformation T is one-to-one on its coimage, and the coimage maps isomorphically onto the image...
abelian category (a special kind of preadditive category) the image and coimage of a morphism f are given by im ( f ) = ker ( coker f ) , coim ...
theorem, which states that: C ≅ B/ker r ≅ B/q(A) (i.e., C isomorphic to the coimage of r or cokernel of q) to: B = q(A) ⊕ u(C) ≅ A ⊕ C where the first isomorphism...
epimorphism followed by a monomorphism. This epimorphism is called the coimage of f, while the monomorphism is called the image of f. Subobjects and quotient...
study of algebraic objects. Homomorphisms Kernels and cokernels Image and coimage Epimorphisms and monomorphisms Isomorphisms Isomorphism theorems There...
X given by g ↦ g · x. The image of this map is the orbit of x and the coimage is the set of all left cosets of Gx. The standard quotient theorem of set...
that states a weak structure is equivalent to a strict structure. coimage The coimage of a morphism f: X → Y is the coequalizer of X × Y X ⇉ X {\displaystyle...
{\displaystyle \operatorname {Coim} _{\infty }\varphi } are called the nodal coimage of φ {\displaystyle \varphi } , im ∞ φ {\displaystyle \operatorname {im}...
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