Bicategories of Action Groupoids
Differential Geometry
2024-05-01 v2
Abstract
We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences \`a la Pronk, localising using surjective submersive equivariant weak equivalences and anafunctors \`a la Roberts, and localising at all weak equivalences. These constructions generalise the known case of representable orbifold groupoids. We also show that any weak equivalence between action Lie groupoids is isomorphic to the composition of two particularly nice forms of equivariant weak equivalences.
Cite
@article{arxiv.2208.06281,
title = {Bicategories of Action Groupoids},
author = {Carla Farsi and Laura Scull and Jordan Watts},
journal= {arXiv preprint arXiv:2208.06281},
year = {2024}
}
Comments
27 pages; v2 is a version more appropriate for publication, and is streamlined. However, v1 has more details for many of the proofs