-
codomain of f by the
image of f. The
dimension of the
cokernel is
called the
corank of f.
Cokernels are dual to the
kernels of
category theory,
hence the...
- in
which morphisms and
objects can be
added and in
which kernels and
cokernels exist and have
desirable properties. The
motivating prototypical example...
-
which all biproducts, kernels, and
cokernels exist is
called pre-abelian.
Further facts about kernels and
cokernels in
preadditive categories that are...
- the
snake lemma does not. Indeed,
arbitrary cokernels do not exist. However, one can
replace cokernels by (left)
cosets A′/ima{\displaystyle A'/\operatorname...
-
specifically because of the
existence of
kernels and
cokernels.
Although kernels and
cokernels are
special kinds of
equalisers and coequalisers, a pre-abelian...
- with the
inclusion homomorphism i : K → A. The same is true for
cokernels; the
cokernel of f is the
quotient group C = B / f(A)
together with the natural...
-
quotient objects (also
called quotient algebras in
universal algebra, and
cokernels in
category theory). For many
types of
algebraic structure, the fundamental...
-
objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and
quotients Pushout Direct limit...
- B ⊔C A. In an
abelian category all
pushouts exist, and they
preserve cokernels in the
following sense: if (P, i1, i2) is the
pushout of f : Z → X and...
-
invariant of a
linear transformation f : V → W {\textstyle f:V\to W} is the
cokernel,
which is
defined as
coker ( f ) := W / f ( V ) = W / im ( f ) . {\displaystyle...
