Publication details
CELLULAR CATEGORIES AND STABLE INDEPENDENCE
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Symbolic Logic |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1017/jsl.2022.40 |
| Doi | http://dx.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. |
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