Bicategories of Action Groupoids

Fuente: arXiv
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Main Authors: Farsi, Carla, Scull, Laura, Watts, Jordan
Format: Preprint
Published: 2022
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author Farsi, Carla
Scull, Laura
Watts, Jordan
author_facet Farsi, Carla
Scull, Laura
Watts, Jordan
contents 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 à la Pronk, localising using surjective submersive equivariant weak equivalences and anafunctors à 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.
format Preprint
id arxiv_https___arxiv_org_abs_2208_06281
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Bicategories of Action Groupoids
Farsi, Carla
Scull, Laura
Watts, Jordan
Differential Geometry
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 à la Pronk, localising using surjective submersive equivariant weak equivalences and anafunctors à 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.
title Bicategories of Action Groupoids
topic Differential Geometry
url https://arxiv.org/abs/2208.06281