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@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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