Cosmological unstraightening
Abstract
The unstraightening construction due to Lurie establishes an equivalence between presheaves and fibrations, using one prominent model of $(\infty, 1)$-categories, namely quasi-categories. In this work we generalize this result by proving that for all $\infty$-cosmoi of $(\infty, 1)$-categories in the sense of Riehl and Verity, which includes quasi-categories but also complete Segal spaces or $1$-complicial sets, their corresponding notions of fibrations and presheaves are biequivalent $\infty$-cosmoi via a natural zig-zag of cosmological biequivalences. The major idea that makes this possible is a lift of the quasi-categorical unstraightening construction to a cosmological biequivalence.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Noncommutative and Quantum Gravity Theories
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Homology Homotopy and Applications
- Publisher
- International Press of Boston
- Volume
- 28
- Issue
- 3
- Pages
- 205–216
- Publication date
- 1 January 2026
- Language
- EN