From fractions to complete Segal spaces
arXiv:1409.8192 · doi:10.4310/HHA.2015.v17.n1.a16
Abstract
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.
21 pages, LaTeX. Changes in v3: added some expository material, following suggestions by anonymous referee. (N.B. numbering has changed.)