2-Cartesian fibrations II: The Grothendieck construction
Fernando Abellán García, Walker H. Stern
Given a scaled simplicial set $S$ we construct a 2-categorical version of the
straightening-unstraightening adjunction furnishing an equivalence between the
$\infty$-bicategory of outer 2-Cartesian fibrations over $S$ and the
$\infty$-bicategory of contravariant functors $S^{\operatorname{op}}\to
\mathbb{B}\!\operatorname{icat}_{\infty}$ with values in the
$\infty$-bicategory of $\infty$-bicategories. We use this technology to
characterize cofinal functors of $\infty$-bicategories via variants of the
conditions of Quillen's Theorem A.