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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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