Epimorphism classes and relatively maximal metrics in large-scale geometry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918249070854144 |
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| author | Tang, Robert |
| author_facet | Tang, Robert |
| contents | We consider epimorphisms and several variant notions -- split, effective, regular, strong, and extremal -- and determine which of these coincide in the metric coarse and coarsely Lipschitz categories. In particular, we characterise extremal epis in the coarsely Lipschitz category via a relative maximality condition on the codomain metric; this can be viewed as a morphism-relative analogue of Rosendal's maximal metrics for topological groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Epimorphism classes and relatively maximal metrics in large-scale geometry Tang, Robert Metric Geometry Category Theory Group Theory 51F30, 20F65 We consider epimorphisms and several variant notions -- split, effective, regular, strong, and extremal -- and determine which of these coincide in the metric coarse and coarsely Lipschitz categories. In particular, we characterise extremal epis in the coarsely Lipschitz category via a relative maximality condition on the codomain metric; this can be viewed as a morphism-relative analogue of Rosendal's maximal metrics for topological groups. |
| title | Epimorphism classes and relatively maximal metrics in large-scale geometry |
| topic | Metric Geometry Category Theory Group Theory 51F30, 20F65 |
| url | https://arxiv.org/abs/2512.13378 |