The Bicategory of Lie Groupoids within Diffeological Groupoids
Abstract
We consider the localisation of the 2-category of diffeological groupoids at weak equivalences from the perspective of anafunctors, and with this language, prove that the localisation of the 2-category of Lie groupoids is an essentially full sub-bicategory of that of diffeological groupoids. In particular, we solve the open problem affirmatively of whether two Lie groupoids that are diffeologically Morita equivalent are Morita equivalent in the usual Lie sense.
Keywords
Cite
@article{arxiv.2206.12730,
title = {The Bicategory of Lie Groupoids within Diffeological Groupoids},
author = {Jordan Watts},
journal= {arXiv preprint arXiv:2206.12730},
year = {2026}
}
Comments
30 pages; v4 has a new subsection on foliations and minor edits; v3 is a condensed version of v2, focusing on anafunctors and bibundles and new results, but without the bicategorical detail; v2 (84 pages) is essentially the same as v1 with some small modifications to the introduction and typographical corrections. To appear in the Journal of Geometry & Physics