CATEGORY OF PRESHEAVES OF A LIE GROUPOID AND REPRESENTATION OF LIE GROUPOIDS

Abstract

A representation of a Lie groupoid G := G ⇒ M is a Lie groupoid morphism of G to a Lie groupoid of manifolds. In this article, we provide a representation of a Lie groupoid G via the functor category of presheaves of G and their equivalence to ManG, the Lie groupoid of right G-manifolds and right G-manifold morphisms.