2-Cartesian fibrations II: A Grothendieck construction for $\infty$-bicategories

Autor:	Abellán, Fernando, Stern, Walker H.
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Mathematics - Category Theory
Druh dokumentu:	Working Paper
Popis:	In this work, we conclude our study of fibred $\infty$-bicategories by providing a Grothendieck construction in this setting. Given a scaled simplicial set $S$ (which need not be fibrant) we construct a 2-categorical version of Lurie's straightening-unstraightening adjunction, thereby furnishing an equivalence between the $\infty$-bicategory of 2-Cartesian fibrations over $S$ and the $\infty$-bicategory of contravariant functors $S^{\operatorname{op}} \to \mathbb{B}\mathbf{\!}\operatorname{icat}_\infty$ with values in the $\infty$-bicategory of $\infty$-bicategories. We provide a relative nerve construction in the case where the base is a 2-category, and use this to prove a comparison to existing bicategorical Grothendieck constructions. Comment: Comments welcome! v2: This version only includes the Grothendieck construction. The results regarding cofinality are now appearing in a separate paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.09589 Zobrazit plný text záznamu View this record from Arxiv