Epimorphism classes and relatively maximal metrics in large-scale geometry
Metric Geometry
2025-12-16 v1 Category Theory
Group Theory
Abstract
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.
Cite
@article{arxiv.2512.13378,
title = {Epimorphism classes and relatively maximal metrics in large-scale geometry},
author = {Robert Tang},
journal= {arXiv preprint arXiv:2512.13378},
year = {2025}
}
Comments
17 pages, 1 figure