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.

References in corpus (2)

• Higher Topos Theory
• All about the Grothendieck construction

Cited by in corpus (6)

• Parametrized higher category theory
• All about the Grothendieck construction
• Fibrations of $\infty$-categories
• A bivariant Yoneda lemma and $(\infty ,2)$-categories of correspondences
• Noncommutative Differential K-theory
• Yoneda Lemma for $\mathcal{D}$-Simplicial Spaces