CELLULAR CATEGORIES AND STABLE INDEPENDENCE

Varování

Publikace nespadá pod Fakultu sportovních studií, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.

Autoři	LIEBERMAN Michael Joseph ROSICKÝ Jiří VASEY Sebastien
Rok publikování	2023
Druh	Článek v odborném periodiku
Časopis / Zdroj	Journal of Symbolic Logic
Fakulta / Pracoviště MU	Přírodovědecká fakulta
Citace
www	https://doi.org/10.1017/jsl.2022.40
Doi	http://dx.doi.org/10.1017/jsl.2022.40
Klíčová slova	cellular categories; forking; stable independence; abstract elementary class; cofibrantly generated; roots of Ext
Popis	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.
Související projekty:	Injektivita a monády v algebře a topologii