Stacky Lie Groups
Department of Mathematics, University of California, Berkeley, CA 94720, USA
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Correspondence: Correspondence to be sent to: christian.blohmann{at}mathematik.uni-regensburg.de
Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles is a categorical property which is sufficient and necessary for the existence of products. Stacky Lie groups are defined as group objects in this weak 2-category. Introducing a graphic notation, it is shown that for every stacky Lie monoid there is a natural morphism, called the preinverse, which is a Morita equivalence if and only if the monoid is a stacky Lie group. As an example, we describe explicitly the stacky Lie group structure of the irrational Kronecker foliation of the torus.