Categories with norms
Category Theory
2017-05-30 v1
Abstract
We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a category, generalizing pseudo-metrics and group valuations. In this new context, we discuss topics like Cauchy completion and the Banach Contraction Principle.
Keywords
Cite
@article{arxiv.1705.10189,
title = {Categories with norms},
author = {Wiesław Kubiś},
journal= {arXiv preprint arXiv:1705.10189},
year = {2017}
}
Comments
20 pages