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… Expand
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