Approximate injectivity and smallness in metric-enriched categories
| Autor: | Jiří Rosický, Jiří Adámek |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Pure mathematics Algebra and Number Theory 010102 general mathematics 0211 other engineering and technologies Banach space 021107 urban & regional planning Mathematics - Category Theory 02 engineering and technology Space (mathematics) 01 natural sciences Injective function Mathematics - Functional Analysis Morphism Mathematics::Category Theory Metric (mathematics) Category of metric spaces Uniqueness 0101 mathematics 18C35 18D20 46M10 Mathematics |
| Popis: | 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. Comment: 36 pages |
| Databáze: | OpenAIRE |
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