On the Dold-Kan correspondence

Gustavo Jasso (University of Bonn)

Wednesday 14th November, 2018 16:00-17:00 Maths 311B


The classical Dold-Kan correspondence is an explicit equivalence of categories between the category of simplicial abelian groups and the category of connective chain complexes of abelian groups. There are two recent variants of this correspondence. In the first variant, due to Lurie, the category of abelian groups is replaced by the $\infty$-category of spectra; in the second variant, due to Dyckerhoff, one considers instead the $(\infty,2)$-category of stable $\infty$-categories. In this talk I will discuss, using only rudiments of $\infty$-category theory, common aspects of these correspondences and explain how these fit within the conjectural framework of categorified homological algebra. The talk is based on join work in progress with Tobias Dyckerhoff and Tashi Walde.

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