Homology, Homotopy and Applications
Volume 17 (2015)
From fractions to complete Segal spaces
Pages: 321 – 338
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.