Work

2-CARTESIAN FIBRATIONS II: A GROTHENDIECK CONSTRUCTION FOR $\infty $ -BICATEGORIES

Year: 2025

Type: article

Abstract: 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 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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748025101436

Authors: Fernando Abellán, Walker H. Stern

Institutions: Norwegian University of Science and Technology, Technical University of Munich

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, University of Virginia, Volkswagen Foundation