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Approximate injectivity and smallness in metric-enriched categories

The result's identifiers

  • 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>

Alternative languages

  • 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 -&gt; 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

Classification

  • 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

Result continuities

  • 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)

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Pure and Applied Algebra

  • ISSN

    0022-4049

  • e-ISSN

  • Volume of the periodical

    226

  • Issue of the periodical within the volume

    6

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    30

  • Pages from-to

    106974

  • UT code for WoS article

    000744249900002

  • EID of the result in the Scopus database

    2-s2.0-85119609485