CELLULAR CATEGORIES AND STABLE INDEPENDENCE

J 2023

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

LIEBERMAN, Michael Joseph, Jiří ROSICKÝ and Sebastien VASEY

Basic information

Original name

CELLULAR CATEGORIES AND STABLE INDEPENDENCE

Authors

LIEBERMAN, Michael Joseph (840 United States of America, guarantor), Jiří ROSICKÝ (203 Czech Republic, belonging to the institution) and Sebastien VASEY

Edition

Journal of Symbolic Logic, Cambridge, Cambridge University Press, 2023, 0022-4812

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.600 in 2022

RIV identification code

RIV/00216224:14310/23:00134133

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1017/jsl.2022.40

UT WoS

000896800600001

Keywords in English

cellular categories; forking; stable independence; abstract elementary class; cofibrantly generated; roots of Ext

Abstract

V originále

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin–Eklof–Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický.

Links

GA19-00902S, research and development project

Name: Injektivita a monády v algebře a topologii

Investor: Czech Science Foundation

Citovat

LIEBERMAN, Michael Joseph, Jiří ROSICKÝ and Sebastien VASEY. CELLULAR CATEGORIES AND STABLE INDEPENDENCE. Journal of Symbolic Logic. Cambridge: Cambridge University Press, 2023, vol. 88, No 2, p. 811-834. ISSN 0022-4812. Available from: https://dx.doi.org/10.1017/jsl.2022.40.

@article{2287020,
   author = {Lieberman, Michael Joseph and Rosický, Jiří and Vasey, Sebastien},
   article_location = {Cambridge},
   article_number = {2},
   doi = {http://dx.doi.org/10.1017/jsl.2022.40},
   keywords = {cellular categories; forking; stable independence; abstract elementary class; cofibrantly generated; roots of Ext},
   language = {eng},
   issn = {0022-4812},
   journal = {Journal of Symbolic Logic},
   title = {CELLULAR CATEGORIES AND STABLE INDEPENDENCE},
   url = {https://doi.org/10.1017/jsl.2022.40},
   volume = {88},
   year = {2023}
}

TY  - JOUR
ID  - 2287020
AU  - Lieberman, Michael Joseph - Rosický, Jiří - Vasey, Sebastien
PY  - 2023
TI  - CELLULAR CATEGORIES AND STABLE INDEPENDENCE
JF  - Journal of Symbolic Logic
VL  - 88
IS  - 2
SP  - 811-834
EP  - 811-834
PB  - Cambridge University Press
SN  - 00224812
KW  - cellular categories
KW  - forking
KW  - stable independence
KW  - abstract elementary class
KW  - cofibrantly generated
KW  - roots of Ext
UR  - https://doi.org/10.1017/jsl.2022.40
N2  - We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin–Eklof–Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický.
ER  -

LIEBERMAN, Michael Joseph, Jiří ROSICKÝ and Sebastien VASEY. CELLULAR CATEGORIES AND STABLE INDEPENDENCE. \textit{Journal of Symbolic Logic}. Cambridge: Cambridge University Press, 2023, vol.~88, No~2, p.~811-834. ISSN~0022-4812. Available from: https://dx.doi.org/10.1017/jsl.2022.40.

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