Fibration categories are fibrant relative categories

Meier, Lennart

doi:10.2140/agt.2016.16.3271

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Fibration categories are fibrant relative categories

Lennart Meier

Algebraic & Geometric Topology 16 (2016) 3271–3300

DOI: 10.2140/agt.2016.16.3271

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

Volume 16, issue 6 (2016)