Simplicial group

Similarly, a simplicial abelian group is a simplicial object in the category of abelian groups.

The Dold–Kan correspondence says that a simplicial abelian group may be identified with a chain complex.

In fact it can be shown that any simplicial abelian group

is non-canonically homotopy equivalent to a product of Eilenberg–MacLane spaces,

Eckmann (1945) discusses a simplicial analogue of the fact that a cohomology class on a Kähler manifold has a unique harmonic representative and deduces Kirchhoff's circuit laws from these observations.