The bicategory of groupoid correspondences
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866929561431703552 |
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| author | Antunes, Celso Ko, Joanna Meyer, Ralf |
| author_facet | Antunes, Celso Ko, Joanna Meyer, Ralf |
| contents | We define a bicategory with étale, locally compact groupoids as objects and suitable correspondences, that is, spaces with two commuting actions as arrows; the 2-arrows are injective, equivariant continuous maps. We prove that the usual recipe for composition makes this a bicategory, carefully treating also non-Hausdorff groupoids and correspondences. We extend the groupoid C*-algebra construction to a homomorphism from this bicategory to that of C*-algebra correspondences. We describe the C*-algebras of self-similar groups, higher-rank graphs, and discrete Conduché fibrations in our setup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10869 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The bicategory of groupoid correspondences Antunes, Celso Ko, Joanna Meyer, Ralf Operator Algebras 46L55 We define a bicategory with étale, locally compact groupoids as objects and suitable correspondences, that is, spaces with two commuting actions as arrows; the 2-arrows are injective, equivariant continuous maps. We prove that the usual recipe for composition makes this a bicategory, carefully treating also non-Hausdorff groupoids and correspondences. We extend the groupoid C*-algebra construction to a homomorphism from this bicategory to that of C*-algebra correspondences. We describe the C*-algebras of self-similar groups, higher-rank graphs, and discrete Conduché fibrations in our setup. |
| title | The bicategory of groupoid correspondences |
| topic | Operator Algebras 46L55 |
| url | https://arxiv.org/abs/2111.10869 |