Approximate injectivity and smallness in metric-enriched categories

DOI10.1016/J.JPAA.2021.106974arXiv2006.01399WikidataQ123181283 ScholiaQ123181283MaRDI QIDQ6341885

Publication date: 2 June 2020

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.

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Isometric theory of Banach spaces (46B04) Categories, functors in functional analysis (46M15) Accessible and locally presentable categories (18C35) Enriched categories (over closed or monoidal categories) (18D20)

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