Pushouts of extensions of groupoids by bundles of abelian groups

@article{Ionescu2021PushoutsOE,
  title={Pushouts of extensions of groupoids by bundles of abelian groups},
  author={Marius Ionescu and Alex Kumjian and Jean N. Renault and Aidan Sims and Dana P. Williams},
  journal={New Zealand Journal of Mathematics},
  year={2021}
}
We analyse extensions $\Sigma$ of groupoids G by bundles A of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid G by a given bundle A. There is a natural action of Sigma on the dual of A, yielding a corresponding transformation groupoid. The pushout of this transformation groupoid by the natural map from the fibre product of A with its dual to the Cartesian product of the dual with the circle is a twist over… 
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