Fat Lie theory

par Lennart Obster (Coimbra)

vendredi 20 mars 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

In the talk, we will discuss a new point of view of representation theory of Lie groupoids and algebroids: fat Lie theory. We introduce the category of fat extensions, and we show that it is equivalent to the category of VB-groupoids (vector bundle groupoids). We also introduce abstract representations up to homotopy (ruths), which allows us to realise the well-known equivalence between VB-groupoids and 2-term ruths via a type of Serre-Swan theorem. Now, Cattafi and Garmendia showed that there is a one-to-one correspondence between general linear PB-groupoids and VB-groupoids. The next part of the talk will be about upgrading this correspondence to an equivalence, and we do so by using fat extensions. Lastly, we introduce core extensions, which are intimately related to fat extensions. We indicate how such objects correspond to vertically/horizontally core-transitive double groupoids (which generalises work by Brown, Jotz-Lean and Mackenzie) and that, therefore, regular fat extensions also correspond to general linear double groupoids. Throughout, we make comments about the infinitesimal side of things (for Lie algebroids).