Dold–Kan correspondence
In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence (named after Albrecht Dold and Daniel Kan) states that there is an equivalence between the category of (nonnegatively graded) chain complexes and the category of simplicial abelian groups. Moreover, under the equivalence, the n {\displaystyle n} th homology group of a chain complex is the n {\displaystyle n} th homotopy group of the corresponding simplicial abelian group, and a chain homotopy corresponds to a simplicial homotopy.