-
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...
-
which all biproducts, kernels, and
cokernels exist is
called pre-abelian.
Further facts about kernels and
cokernels in
preadditive categories that are...
- zero object. Then
there is an
exact sequence relating the
kernels and
cokernels of a, b, and c: ker a ⟶ ker b ⟶ ker c ⟶ d
coker a...
- in
which morphisms and
objects can be
added and in
which kernels and
cokernels exist and have
desirable properties. The
motivating prototypical example...
-
quotient objects (also
called quotient algebras in
universal algebra, and
cokernels in
category theory). For many
types of
algebraic structure, the fundamental...
-
specifically because of the
existence of
kernels and
cokernels.
Although kernels and
cokernels are
special kinds of
equalisers and coequalisers, a pre-abelian...
- the semi-stable kernels. Dually,
cokernels,
which are
stable under arbitrary pullbacks, are
called semi-stable
cokernels. Let f {\displaystyle f} be a morphism...
- 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...
- they are
closed under operations such as
taking kernels, images, and
cokernels. The quasi-coherent
sheaves are a
generalization of
coherent sheaves and...
-
notion of an
exact sequence makes sense in any
category with
kernels and
cokernels. The most
common type of
exact sequence is the
short exact sequence. This...
