Lecture 9 - Óscar Carballal (UCM) - Constructions and equivalences in the category of Lie groupoids

Ninth lecture from the Reading Groupoid (readinggroupoid.org) Abstract: In this talk, I will present several constructions in the category of Lie groupoids, including pullbacks, fibered products, and homotopy pullbacks. Then, some notions of equivalence between Lie groupoids will be discussed, focusing in particular on Morita equivalence, which plays a central rôle in the modern approach to differentiable stacks, foliation theory, and geometric quantisation. Several of the constructions and equivalence notions will be illustrated through examples coming from the theory of foliations.