Algebraic & Geometric Topology

Homotopy theory of cocomplete quasicategories

Karol Szumiło

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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

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

Received: 29 June 2015
Revised: 30 April 2016
Accepted: 4 July 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

homotopy theory quasicategory homotopy colimit cofibration category


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

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