Axel Osmond - The over-topos at a model
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 01/07/2021

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/OsmondSlidesToposesOnline.pdf

For a model of a geometric theory in a Grothendieck topos, we can construct the over-topos of this model classifying homomorphisms above it. In this talk, we provide a site theoretic description of this construction. In the case of a set-valued model, a site will be provided by the category of global elements together with a certain antecedents topology, and we can describe a canonical geometric theory classified by this over-topos. In the general case, one must consider a more complicated category of generalized elements ; an antecedent topology then can be recovered through a notion of lifted topology, whose construction can be understood in the framework of stacks and comorphisms of sites.

This is joint work with Olivia Caramello.