Moore complex #
We construct the normalized Moore complex, as a functor
SimplicialObject C ⥤ ChainComplex C ℕ
,
for any abelian category C
.
The n
-th object is intersection of
the kernels of X.δ i : X.obj n ⟶ X.obj (n-1)
, for i = 1, ..., n
.
The differentials are induced from X.δ 0
,
which maps each of these intersections of kernels to the next.
This functor is one direction of the Dold-Kan equivalence, which we're still working towards.
References #
- https://stacks.math.columbia.edu/tag/0194
- https://ncatlab.org/nlab/show/Moore+complex
The definitions in this namespace are all auxiliary definitions for NormalizedMooreComplex
and should usually only be accessed via that.
The normalized Moore complex in degree n
, as a subobject of X n
.
Instances For
The differentials in the normalized Moore complex.
Instances For
The normalized Moore complex functor, on objects.
Instances For
The normalized Moore complex functor, on morphisms.
Instances For
The (normalized) Moore complex of a simplicial object X
in an abelian category C
.
The n
-th object is intersection of
the kernels of X.δ i : X.obj n ⟶ X.obj (n-1)
, for i = 1, ..., n
.
The differentials are induced from X.δ 0
,
which maps each of these intersections of kernels to the next.