{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/categorical-characterisations-of-quasi","title":"Categorical characterisations of quasi-isometric embeddings","arxiv_id":"2411.08501","date":"2024-11-13","proceeding":null,"authors":["Robert Tang"],"abstract":"We characterise the (closeness classes of) quasi-isometric embeddings as the regular monomorphisms in the coarsely Lipschitz category, formalising the notion that they are isomorphisms onto their image. Furthermore, we prove that the coarsely Lipschitz category is coregular, and hence admits an (Epi, RegMono)--orthogonal factorisation system. Consequently, quasi-isometric embeddings are equivalently characterised as the effective, strong, or extremal monomorphisms. Finally, we prove that the coarsely Lipschitz category is not coexact in the sense of Barr.","url_abs":"https://arxiv.org/abs/2411.08501v1","url_pdf":"https://arxiv.org/pdf/2411.08501v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"categorical-characterisations-of-quasi","repo_url":"https://github.com/rob-tang/rob-tang.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}