This evening, at 9pm CET, I will give an online talk on “Relative topos theory via stacks” at the University of Wisconsin Logic Seminar. Many thanks to the organizers of this Seminar, in particular to Prof. Steffen Lempp, for this invitation!

You may attend the talk as follows:

Zoom link to local UW logic seminar
Meeting ID: 986 3594 0882
Passcode: 003073

Abstract: In this talk, based on joint work with Riccardo Zanfa, we shall introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of (relatively small) toposes over the topos of sheaves on a given site (C, J) and that of C-indexed categories. This represents a wide generalization of the classical adjunction between presheaves on a topological space and bundles over it, and allows one to interpret several constructions on sheaves and stacks in a geometrical way; in particular, it leads to fibrational descriptions of direct and inverse images of sheaves and stacks, as well as to a geometric understanding of the sheafification process. It also naturally allows one to regard any Grothendieck topos as a ‘petit’ topos associated with a ‘gros’ topos, thereby providing an answer to a problem posed by Grothendieck in the seventies.