Quasi-Categories vs. Segal Spaces: Cartesian Edition
Category Theory
2021-08-24 v3 Algebraic Topology
Abstract
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces, on bisimplicial sets, on marked simplicial spaces. The main way to prove these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal-Tierney and the straightening construction due to Lurie.
Keywords
Cite
@article{arxiv.2102.05192,
title = {Quasi-Categories vs. Segal Spaces: Cartesian Edition},
author = {Nima Rasekh},
journal= {arXiv preprint arXiv:2102.05192},
year = {2021}
}
Comments
Final version, Published in Journal of Homotopy and Related Structures