Categorical approach to rigidity of Roe-like algebras of coarse spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912268005933056 |
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| author | Krutoy, Kostyantyn |
| author_facet | Krutoy, Kostyantyn |
| contents | We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such $*$-functors between approximable categories and prove that the functor associating each locally finite coarse space with its approximable category is full and faithful. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical approach to rigidity of Roe-like algebras of coarse spaces Krutoy, Kostyantyn Operator Algebras Metric Geometry 53C24, 51F30, 52C25, 51K05 We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such $*$-functors between approximable categories and prove that the functor associating each locally finite coarse space with its approximable category is full and faithful. |
| title | Categorical approach to rigidity of Roe-like algebras of coarse spaces |
| topic | Operator Algebras Metric Geometry 53C24, 51F30, 52C25, 51K05 |
| url | https://arxiv.org/abs/2503.07398 |