Categorical characterisations of quasi-isometric embeddings
Metric Geometry
2024-11-14 v1 Category Theory
Group Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.2411.08501,
title = {Categorical characterisations of quasi-isometric embeddings},
author = {Robert Tang},
journal= {arXiv preprint arXiv:2411.08501},
year = {2024}
}
Comments
19 pages, 1 appendix