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Fibration categories are fibrant relative categories

Lennart Meier

Algebraic & Geometric Topology 16 (2016) 3271–3300
Abstract

A relative category is a category with a chosen class of weak equivalences. Barwick and Kan produced a model structure on the category of all relative categories, which is Quillen equivalent to the Joyal model structure on simplicial sets and the Rezk model structure on simplicial spaces. We will prove that the underlying relative category of a model category or even a fibration category is fibrant in the Barwick–Kan model structure.

Keywords
fibration categories, model categories, relative categories
Mathematical Subject Classification 2010
Primary: 18D99, 55U10, 55U35
References
Publication
Received: 20 April 2015
Revised: 1 April 2016
Accepted: 28 April 2016
Published: 15 December 2016
Authors
Lennart Meier
Mathematisches Institut
University of Bonn
Endenicher Allee 60
D-53115 Bonn
%53123 seems incorrect Germany
http://www.math.uni-bonn.de/people/lmeier