Functorial aspects of the reconstruction of Lie groupoids from their bisections
arXiv:1506.05587 · doi:10.1017/S1446788716000021
Abstract
To a Lie groupoid over a compact base, the associated group of bisection is an (infinite-dimensional) Lie group. Moreover, under certain circumstances one can reconstruct the Lie groupoid from its Lie group of bisections. In the present article we consider functorial aspects of these construction principles. The first observation is that this procedure is functorial (for morphisms fixing the base). Moreover, it gives rise to an adjunction between the category of Lie groupoids over a fixed base and the category of Lie groups acting on the base. In the last section we then show how to promote this adjunction to almost an equivalence of categories.
16 pages, LaTex, this is a companion to arXiv:1506.05415
References in corpus (4)
- Abelian extensions of infinite-dimensional Lie groups
- Fundamentals of submersions and immersions between infinite-dimensional manifolds
- (Re)constructing Lie groupoids from their bisections and applications to prequantisation
- Differential Calculus, Manifolds and Lie Groups over Arbitrary Infinite Fields