A user's guide to co/cartesian fibrations

Abstract

We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely *within the $\infty$-category of $\infty$-categories*. We prove this is suitably compatible with the corresponding quasicategorical (and in particular, model-dependent) notions studied by Joyal and Lurie.