Séminaire d'algèbre et de géométrie du 09-04-2026
Exposé de Santiago Toro Oquendo
Le 09-04-2026 à 15:00, en P108 et en ligne.The Homotopy Theory of Cartesian 2-Fibrations
Informations de connexion
Zoom
Résumé
The Grothendieck construction plays a central role in category theory, providing a bridge between indexed categories and fibered categories and allowing techniques from both perspectives to be applied. In recent work (2023), L. Moser and M. Sarazola constructed a model category structure whose fibrant objects encode Grothendieck fibrations over a fixed category C. Using markings, they define this structure on the slice category Cat/C and via a marked version of the Grothendieck construction show that it is Quillen equivalent to the projective model structure on a suitable category of functors. The goal of this talk is to explain how this model structure can be extended to the 2-categorical setting so as to capture Michael Buckley’s notion of 2-fibration as the fibrant objects. I will outline the main ideas behind this extension and discuss several obstructions to obtaining a Quillen equivalence analogous to the one in the 1-categorical case. If time permits, I will also present comparison results with related constructions in (∞,2)-categories. This is joint work in progress with M. Sarazola, P. Verdugo, J. Nickel, C. Bardomiano, and D. Teixeira.