A categorified Dold–Kan correspondence

Abstract: The transition from Betti numbers to homology groups was a decisive step turning the subject previously known as combinatorial topology into what is nowadays called algebraic topology. Further, the accompanying foundations of homological algebra are of universal nature so that they can be applied in a wide range of other mathematical subjects where they have come to play an essential role.

In this talk, we discuss the idea of categorifying homological algebra one step further, replacing complexes of abelian groups by complexes of enhanced triangulated categories, illustrated by a concrete result: a categorification of the classical Dold–Kan correspondence

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)