English

A pullback diagram in the coarse category

Metric Geometry 2022-03-15 v2 Category Theory

Abstract

This paper studies the asymptotic product of two metric spaces. It is well defined if one of the spaces is visual or if both spaces are geodesic. In this case the asymptotic product is the pullback of a limit diagram in the coarse category. Using this product construction we can define a homotopy theory on coarse metric spaces in a natural way. We prove that all finite colimits exist in the coarse category.

Keywords

Cite

@article{arxiv.1907.02961,
  title  = {A pullback diagram in the coarse category},
  author = {Elisa Hartmann},
  journal= {arXiv preprint arXiv:1907.02961},
  year   = {2022}
}

Comments

20 pages

R2 v1 2026-06-23T10:13:28.390Z