English

Approximate injectivity and smallness in metric-enriched categories

Category Theory 2022-02-08 v2 Functional Analysis

Abstract

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of constructions known from that category and the category of Banach spaces. For every class of morphisms satisfying a mild smallness condition we prove the corresponding approximate-injectivity class is weakly reflective, and we study the properties of the reflection morphisms. As an application we present a new categorical proof of the essential uniqueness of the Gurarii space.

Keywords

Cite

@article{arxiv.2006.01399,
  title  = {Approximate injectivity and smallness in metric-enriched categories},
  author = {Jiří Adámek and Jiří Rosický},
  journal= {arXiv preprint arXiv:2006.01399},
  year   = {2022}
}

Comments

36 pages

R2 v1 2026-06-23T15:58:57.654Z