English

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

R2 v1 2026-06-22T20:02:14.433Z