From double groupoids to 2-groupoids

0.07
Friday, 3 July, 2009 - 14:30

A double (Lie) groupoid is a groupoid in the category of (Lie) groupoids. A standard example is the fundamental double Lie groupoid of a Lie groupoid. I will describe a functor from the category of double Lie groupoids to the category of simplicial manifolds. In general, the simplicial manifolds that arise in this process are local Lie 2-groupoids. There is a process for turning a local Lie 2-groupoid into a groupoid, but smoothness is lost in general. However, in the above standard example, the resulting groupoid is smooth and agrees with a construction of Moerdijk and Mrcun.

Speaker: 

Rajan Mehta