A short proof of the straightening theorem

Abstract

We provide a short and reasonably self-contained proof of Lurie's straightening equivalence, relating cartesian fibrations over a given $\infty$-category $S$ with contravariant functors from $S$ to the $\infty$-category of small $\infty$-categories.

42 pages, v2: Minor revision following a referee report, to appear in Transactions of the AMS