| In this thesis, we study the notion of action Lie groupoid. we find that every2-vectorspace has a nature action of a Lie group, and then we get an action groupoid. So we build theconnection between the2-vector space and the Lie groupoid theory.In chapter1, I introduce the background of the groupoid and some Preliminaries, likethe notion of a Lie group and the properties of Lie groups and action of Lie groups.In chapter2, I give the definition of the Lie groupoid and discuss some propertiesabout it, and then give some examples of Lie groupoids, especially talking about the actiongroupoid.In chapter3, I give the definition of a2-vector space, and the categorification of thevector space, i.e. the category of addition, subtraction and scalar multiplication.2-vectorspace can give an action groupoid in the end. |
