Riccardo Zanfa - Extending the topological presheaf-bundle adjunction to sites and toposes
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2021-07-01

Talk at the school and conference “Toposes online” (24-30 June 2021):
https://aroundtoposes.com/toposesonline/

Slides:
https://aroundtoposes.com/wp-content/uploads/2021/07/ZanfaSlidesToposesOnline.pdf

Riccardo Zanfa: “Extending the topological presheaf-bundle adjunction to sites and toposes”

A well-known result in topology states that for any topological space X there exists an adjunction between its category of presheaves Psh(X) and the category of bundles over X, i.e. Top/X. The purpose of this talk is to extend this result by replacing X with a small site (C,J), by using the tools of fibrations and of comorphisms of sites. One particularly relevant consequence is a geometric perspective on the sheafification functor a:Psh(C) -- Sh(C,J).


The content of the talk stems from a joint work with Olivia Caramello, Relative topos theory via stacks:
https://arxiv.org/abs/2107.04417