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 ∞-category; the guiding example is an ∞-categorical Dold–Kan correspondence between the ∞-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 Γ-groups and, more generally, the combinatorial categorical equivalences of Lack and Street.