# FUNCTORIAL ASPECTS OF THE RECONSTRUCTION OF LIE GROUPOIDS FROM THEIR BISECTIONS

@article{Schmeding2016FUNCTORIALAO, title={FUNCTORIAL ASPECTS OF THE RECONSTRUCTION OF LIE GROUPOIDS FROM THEIR BISECTIONS}, author={Alexander Schmeding and Christoph Wockel}, journal={Journal of the Australian Mathematical Society}, year={2016}, volume={101}, pages={253 - 276} }

To a Lie groupoid over a compact base $M$ , 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 $M$ ). Moreover, it gives rise to an adjunction between the category of Lie groupoids over $M$ and the…

## 4 Citations

Re)constructing Lie groupoids from their bisections and applications to prequantisation

- Mathematics
- 2015

This paper is about the relation of the geometry of Lie groupoids over a fixed compact manifold and the geometry of their (infinite-dimensional) bisection Lie groups. In the first part of the paper…

The Lie group of vertical bisections of a regular Lie groupoid

- Mathematics
- 2019

Abstract In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and…

A differentiable monoid of smooth maps on Lie groupoids

- Mathematics
- 2017

In this article we investigate a monoid of smooth mappings on the space of arrows of a Lie groupoid and its group of units. The group of units turns out to be an infinite-dimensional Lie group which…

Linking Lie groupoid representations and representations of infinite-dimensional Lie groups

- MathematicsAnnals of Global Analysis and Geometry
- 2019

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of…

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