Fibration categories are fibrant relative categories

Meier, Lennart¹

¹Mathematisches Institut, University of Bonn, Endenicher Allee 60, D-53115 Bonn, %53123 seems incorrect Germany

Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3271-3300

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.3271

Classification : 18D99, 55U10, 55U35
Keywords: fibration categories, model categories, relative categories

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