Homotopy coherent theorems of Dold-Kan type

Autor:	Walde, Tashi
Rok vydání:	2019
Předmět:	Mathematics - Representation Theory Mathematics - Algebraic Topology Mathematics - Category Theory 16D90 18E05 18E30 18G30 18G35 55U10 55U15
Zdroj:	Adv. Math. 398 (2022), 108175
Druh dokumentu:	Working Paper
DOI:	10.1016/j.aim.2021.108175
Popis:	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. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.06368 Zobrazit plný text záznamu View this record from Arxiv