Algebraic & Geometric Topology

Homotopy theory of cocomplete quasicategories

Karol Szumiło

Abstract

We prove that the homotopy theory of cocomplete quasicategories is equivalent to the homotopy theory of cofibration categories. This is achieved by presenting both theories as fibration categories and constructing an explicit exact equivalence between them.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 2 (2017), 765-791.

Dates
Revised: 30 April 2016
Accepted: 4 July 2016
First available in Project Euclid: 19 October 2017

https://projecteuclid.org/euclid.agt/1508431443

Digital Object Identifier
doi:10.2140/agt.2017.17.765

Mathematical Reviews number (MathSciNet)
MR3623671

Zentralblatt MATH identifier
1364.55019

Subjects
Primary: 55U35: Abstract and axiomatic homotopy theory
Secondary: 18G55: Homotopical algebra

Citation

Szumiło, Karol. Homotopy theory of cocomplete quasicategories. Algebr. Geom. Topol. 17 (2017), no. 2, 765--791. doi:10.2140/agt.2017.17.765. https://projecteuclid.org/euclid.agt/1508431443

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