A categorified Dold-Kan correspondence

Author:

Dyckerhoff Tobias

Abstract

AbstractIn this work, we establish a categorification of the classical Dold-Kan correspondence in the form of an equivalence between suitably defined $$\infty $$ -categories of simplicial stable $$\infty $$ -categories and connective chain complexes of stable $$\infty $$ -categories. The result may be regarded as a contribution to the foundations of an emerging subject that could be termed categorified homological algebra.

Funder

Projekt DEAL

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,General Mathematics

Reference17 articles.

1. Abellán García, F., Dyckerhoff, T., Stern, W.: A relative 2-nerve. (2019) arXiv:1910.06223 to appear in Algebr. Geom. Topol

2. Bondal, A., Kapranov, M.: Representable functors, Serre functors, and mutations. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 53(6), 1183–1205 (1989)

3. Dyckerhoff, Tobias, Jasso, Gustavo, Walde, Tashi: Simplicial structures in higher Auslander-Reiten theory. Adv. Math. 355, 106762 (2019)

4. Dyckerhoff, Tobias, Kapranov, Mikhail: Triangulated surfaces in triangulated categories. J. Eur. Math. Soc. (JEMS) 20(6), 1473–1524 (2018)

5. Dyckerhoff, T., Kapranov, M., Schechtman, V., Soibelman, Y.: Topological Fukaya categories with coefficients. in preparation (2017)

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