  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.
