Speaker: Jacopo Emmenegger

Title: Some remarks on groupoids in fibrations

Abstract:

I will explain how to generalise the notion of internal groupoid from categories to fibred categories (i.e. Grothendieck fibrations) and how to use that notion to refine a characterisation of elementary fibrations (aka fibrations with equality). The refinement allows for a neat proof of comonadicity of elementary fibrations over those with finite products. If time allows I will also discuss some properties of this comonad.

This is based on joint work with Fabio Pasquali and Pino Rosolini.