The Dold-Kan correspondence


Venue/Location: C102, VIASM

Speaker: Phạm Khoa Bằng (ĐHKHTN)


The objective of this talk is to introduce to the audiences about the so-called Dold-Kan correspondence theorem, a celebrated result which belongs to the field of simplicial homotopy theory. Loosely, the theorem asserts that there is an equivalence between the category of nonnegative chain complexes and the category of simplicial objects on a given abelian category. The theorem was discovered by A. Dold and D. Kan independently in 1957. Although two categories are equivalent, each category has important invariants and essential aspects, for instance, the latter one contains a lot more combinatorial information. We will start with the language of simplicial objects and then give a concrete proof for the theorem. If time permits, we will show how A. Dold and D. Puppe used this theorem to define derived functors of non-additive functors.