- The
cokernel of a
linear mapping of
vector spaces f : X → Y is the
quotient space Y / im(f) of the
codomain of f by the
image of f. The
dimension of the...
- pre-abelian
category is an
additive category that has all
kernels and
cokernels.
Spelled out in more detail, this
means that a
category C is pre-abelian...
- the
kernel of some morphism, and an
epimorphism is
conormal if it is the
cokernel of some morphism. A
category C is
binormal if it's both
normal and conormal...
- is
again a
kernel and, dually, the
pullback of a
cokernel along arbitrary morphisms is
again a
cokernel. A quasi-abelian
category is an
exact category.[citation...
- B,
while the
cokernel of f is the
coequaliser of f and this zero morphism.
Unlike with
products and coproducts, the
kernel and
cokernel of f are generally...
- in
which morphisms and
objects can be
added and in
which kernels and
cokernels exist and have
desirable properties. The
motivating prototypical example...
-
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...
- The dual
concept to that of
kernel is that of
cokernel. That is, the
kernel of a
morphism is its
cokernel in the
opposite category, and vice versa. As...
-
particularly simple. It is just the
factor group Y / im(f – g). (This is the
cokernel of the
morphism f – g; see the next section). In the
category of topological...
-
theory of
triangulated categories it is a kind of
combined kernel and
cokernel: if the
chain complexes take
their terms in an
abelian category, so that...
