Quasi-Categories vs. Segal Spaces: Cartesian Edition
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.
PDF AbstractCategories
Category Theory
Algebraic Topology
18N60, 18N40, 18N45, 18N55
