Sizes and filtrations in accessible categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114333" target="_blank" >RIV/00216224:14310/20:00114333 - isvavai.cz</a>
Alternative codes found
RIV/00216305:26210/20:PU136846
Result on the web
<a href="https://doi.org/10.1007/s11856-020-2018-8" target="_blank" >https://doi.org/10.1007/s11856-020-2018-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-020-2018-8" target="_blank" >10.1007/s11856-020-2018-8</a>

Result language
angličtina
Original language name
Sizes and filtrations in accessible categories
Original language description
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. We examine set-theoretic problems related to internal sizes and prove several Löwenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all internal sizes of high enough co-finality. We also prove that accessible categories with directed colimits have filtrations: any object of sufficiently high internal size is (the retract of) a colimit of a chain of strictly smaller objects.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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