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Homotopy coherent theorems of Dold-Kan type

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Walde,  Tashi
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Walde, T. (2022). Homotopy coherent theorems of Dold-Kan type. Advances in Mathematics, 398: 108175. doi:10.1016/j.aim.2021.108175.


Cite as: https://hdl.handle.net/21.11116/0000-0009-F979-7
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.