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.
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}
}
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36 pages