Homotopy coherent theorems of Dold-Kan type

Abstract

We establish a large class of homotopy coherent Morita-equivalences of Dold-Kan type relating diagrams with values in any weakly idempotent complete additive $\infty$-category; the guiding example is an $\infty$-categorical Dold-Kan correspondence between the $\infty$-categories of simplicial objects and connective coherent chain complexes. Our results generalize many known 1-categorical equivalences such as the classical Dold-Kan correspondence, Pirashvili's Dold-Kan type theorem for abelian $\Gamma$-groups and, more generally, the combinatorial categorical equivalences of Lack and Street.

31 pages

References in corpus (4)

• Higher Topos Theory
• FI-modules and stability for representations of symmetric groups
• Universality of multiplicative infinite loop space machines
• Combinatorial categorical equivalences of Dold-Kan type

Cited by in corpus (1)

• Coherent cochain complexes and Beilinson t-structures, with an appendix by Achim Krause