On straightening for Segal spaces
Category Theory
2023-09-06 v2 Algebraic Topology
Abstract
The straightening-unstraightening correspondence of Grothendieck--Lurie provides an equivalence between cocartesian fibrations between -categories and diagrams of -categories. We provide an alternative proof of this correspondence, as well as an extension of straightening-unstraightening to all higher categorical dimensions. This is based on an explicit combinatorial result relating two types of fibrations between double categories, which can be applied inductively to construct the straightening of a cocartesian fibration between higher categories.
Keywords
Cite
@article{arxiv.2108.11431,
title = {On straightening for Segal spaces},
author = {Joost Nuiten},
journal= {arXiv preprint arXiv:2108.11431},
year = {2023}
}