Stacky Lie groups

Details Stacky Lie groups Stacky Lie groups

2007-02-14

arxiv.org/abs/math/0702399v3

Int. Mat. Res. Not. (2008) Vol. 2008: article ID rnn082, 51 pages

Mathematics

Differential Geometry

40 pages; definition of group objects in higher categories added; coherence relations for groups in 2-categories given (sectio

Scientific paper

10.1093/imrn/rnn082

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.

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