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.
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