  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.
