Bicategories of Action Groupoids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929330625445888 |
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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 |