# Commit 2021-05-15 08:16 5da114c4

View on Github →feat(algebraic_topology): the Moore complex of a simplicial object (#6308)

## Moore complex

We construct the normalized Moore complex, as a functor
`simplicial_object C ⥤ chain_complex 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.