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Homotopy theory of cocomplete quasicategories

Karol Szumiło

Algebraic & Geometric Topology 17 (2017) 765–791

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.

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homotopy theory, quasicategory, homotopy colimit, cofibration category
Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 18G55
Received: 29 June 2015
Revised: 30 April 2016
Accepted: 4 July 2016
Published: 14 March 2017
Karol Szumiło
Department of Mathematics
University of Western Ontario
1151 Richmond Street
London ON N6A 3K7