Dold–Kan correspondence
In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence 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 homology group of a chain complex is the homotopy group of the corresponding simplicial abelian group, and a chain homotopy corresponds to a simplicial homotopy. (In fact, the correspondence preserves the respective standard model structures.) . There is also an ∞-category-version of a Dold–Kan correspondence.
Wikipage redirect
primaryTopic
Dold–Kan correspondence
In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence 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 homology group of a chain complex is the homotopy group of the corresponding simplicial abelian group, and a chain homotopy corresponds to a simplicial homotopy. (In fact, the correspondence preserves the respective standard model structures.) . There is also an ∞-category-version of a Dold–Kan correspondence.
has abstract
In mathematics, more precisely ...... of a Dold–Kan correspondence.
@en
Link from a Wikipage to an external page
Wikipage page ID
39,431,504
Wikipage revision ID
643,033,208
id
Dold-Kan+correspondence
title
Dold-Kan correspondence
comment
In mathematics, more precisely ...... of a Dold–Kan correspondence.
@en
label
Dold–Kan correspondence
@en