Stacky Lie groups
Abstract
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 example we describe explicitly the stacky Lie group structure of the irrational Kronecker foliation of the torus.
Cite
@article{arxiv.math/0702399,
title = {Stacky Lie groups},
author = {Christian Blohmann},
journal= {arXiv preprint arXiv:math/0702399},
year = {2008}
}
Comments
40 pages; definition of group objects in higher categories added; coherence relations for groups in 2-categories given (section 4)