A short proof of the straightening theorem

Fabian Hebestreit; Gijs Heuts; Jaco Ruit

A short proof of the straightening theorem

Category Theory 2024-12-23 v2 Algebraic Topology

Authors: Fabian Hebestreit , Gijs Heuts , Jaco Ruit

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.

Keywords

straightening theorem cartesian fibrations infinity-categories contravariant functors lurie equivalence

Cite

@article{arxiv.2111.00069,
  title  = {A short proof of the straightening theorem},
  author = {Fabian Hebestreit and Gijs Heuts and Jaco Ruit},
  journal= {arXiv preprint arXiv:2111.00069},
  year   = {2024}
}

Comments

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

A short proof of the straightening theorem

Abstract

Keywords

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