Approximate injectivity and smallness in metric-enriched categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00119372" target="_blank" >RIV/00216224:14310/22:00119372 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/22:00360032
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022404921003157?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022404921003157?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106974" target="_blank" >10.1016/j.jpaa.2021.106974</a>

Result language
angličtina
Original language name
Approximate injectivity and smallness in metric-enriched categories
Original language description
Properties of categories enriched over the category of metric spaces are investigated and applied to a study of well-known constructions of metric and Banach spaces. We prove e.g. that weighted limits and colimits exist in a metric-enriched category iff ordinary limits and colimits exist and ε-(co)equalizers are given by ε-(co)isometries for all ε. An object is called approximately injective w.r.t. a morphism h : A -> A' iff morphisms from A into it are arbitrarily close to those morphisms that factorize through h. We investigate classes of objects specified by their approximate injectivity w.r.t. given morphisms. They are called approximate-injectivity classes. And we also study, conversely, classes of morphisms specified by the property that certain objects are approximately injective w.r.t. them. For every class of morphisms satisfying a mild smallness condition we prove that 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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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