English

From fractions to complete Segal spaces

Category Theory 2015-05-19 v3 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.1409.8192,
  title  = {From fractions to complete Segal spaces},
  author = {Zhen Lin Low and Aaron Mazel-Gee},
  journal= {arXiv preprint arXiv:1409.8192},
  year   = {2015}
}

Comments

21 pages, LaTeX. Changes in v3: added some expository material, following suggestions by anonymous referee. (N.B. numbering has changed.)

R2 v1 2026-06-22T06:08:29.662Z