Approximate injectivity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00101081" target="_blank" >RIV/00216224:14310/18:00101081 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10485-017-9510-2" target="_blank" >http://dx.doi.org/10.1007/s10485-017-9510-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-017-9510-2" target="_blank" >10.1007/s10485-017-9510-2</a>
Alternative languages
Result language
angličtina
Original language name
Approximate injectivity
Original language description
In a locally $lambda$-presentable category, with $lambda$ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are $lambda$-presentable, are known to be characterized by their closure under products, $lambda$-directed colimits and $lambda$-pure subobjects. Replacing the strict commutativity of diagrams by ``commutativity up to $eps$", this paper provides an ``approximate version" of this characterization for categories enriched over metric spaces. It entails a detailed discussion of the needed $eps$-generalizations of the notion of $lambda$-purity. The categorical theory is being applied to the locally $aleph_1$-presentable category of Banach spaces and their linear operators of norm at most 1, culminating in a largely categorical proof for the existence of the so-called Gurarii Banach space.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Categorical Structures
ISSN
0927-2852
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
18
Pages from-to
699-716
UT code for WoS article
000437673800006
EID of the result in the Scopus database
2-s2.0-85038356732