Cellular categories and stable independence

Michael Lieberman; Jiří Rosický; Sebastien Vasey

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arXiv · 1904.05691

Cellular categories and stable independence

Michael Lieberman·Jiří Rosický·Sebastien Vasey

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Abstract

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 Rosick\'y.

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BibTeX RIS

Michael Lieberman, Jiří Rosický, Sebastien Vasey. 2019-04-11. Cellular categories and stable independence. https://arxiv.org/abs/1904.05691

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