Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets
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/

The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos.  The next simplest topology has coverings given by finite disjoint unions.  From an intrinsic perspective, the toposes which arise from such a topology are exactly those which, as a category, have the useful property that they are generated by compact projective objects.  I will discuss some general aspects of this situation, then specialize to a specific example, that of condensed sets. This is joint work with Peter Scholze.