Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

From fractions to complete Segal spaces

Pages: 321 – 338

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n1.a16


Zhen Lin Low (Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, United Kingdom)

Aaron Mazel-Gee (Department of Mathematics, University of California at Berkeley)


We show that the Rezk classification diagram of a relative category admitting a homotopical version of the two-sided calculus of fractions is a Segal space up to Reedy-fibrant replacement. This generalizes the result of Rezk and Bergner on the classification diagram of a closed model category, as well as the result of Barwick and Kan on the classification diagram of a partial model category.


homotopy theory, localization, closed model category, complete Segal space

2010 Mathematics Subject Classification

Primary 18G55. Secondary 18G30, 55U35.

Published 18 May 2015