2020
Sizes and filtrations in accessible categories
LIEBERMAN, Michael; Jiří ROSICKÝ and Sébastien Bernard VASEYBasic information
Original name
Sizes and filtrations in accessible categories
Authors
LIEBERMAN, Michael (840 United States of America, belonging to the institution); Jiří ROSICKÝ (203 Czech Republic, guarantor, belonging to the institution) and Sébastien Bernard VASEY (756 Switzerland)
Edition
Israel Journal of Mathematics, Hebrew University Magnes Press, 2020, 0021-2172
Other information
Language
English
Type of outcome
Article in a journal
Field of Study
10101 Pure mathematics
Country of publisher
Israel
Confidentiality degree
is not subject to a state or trade secret
References:
Impact factor
Impact factor: 0.907
RIV identification code
RIV/00216224:14310/20:00114333
Organization unit
Faculty of Science
UT WoS
000534408400007
EID Scopus
2-s2.0-85085392830
Keywords in English
internal size; presentability rank; existence spectrum; accessibility spectrum; filtrations; singular cardinal hypothesis
Tags
International impact, Reviewed
Changed: 5/3/2021 19:26, prof. RNDr. Jiří Rosický, DrSc.
Abstract
In the original language
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.
Links
| GA19-00902S, research and development project |
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