Extending the topological presheaf-bundle adjunction to sites and toposes
Apparaît dans la collection : Toposes Online
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
