CELLULAR CATEGORIES AND STABLE INDEPENDENCE

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Authors	LIEBERMAN Michael Joseph ROSICKÝ Jiří VASEY Sebastien
Year of publication	2023
Type	Article in Periodical
Magazine / Source	Journal of Symbolic Logic
MU Faculty or unit	Faculty of Science
Citation
web	https://doi.org/10.1017/jsl.2022.40
Doi	https://doi.org/10.1017/jsl.2022.40
Keywords	cellular categories; forking; stable independence; abstract elementary class; cofibrantly generated; roots of Ext
Description	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.
Related projects:	Injektivita a monády v algebře a topologii