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arXiv · 2006.01399

Approximate injectivity and smallness in metric-enriched categories

Jiří Adámek·Jiří Rosický
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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.

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Jiří Adámek, Jiří Rosický. 2020-06-02. Approximate injectivity and smallness in metric-enriched categories. https://arxiv.org/abs/2006.01399

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