Unstable independence from the categorical point of view
arXiv:2310.15804 · doi:10.1016/j.apal.2025.103629
Abstract
We give a category-theoretic construction of simple and NSOP-like independence relations in locally finitely presentable categories, and in the more general locally finitely multipresentable categories. We do so by identifying properties of a class of monomorphisms such that the pullback squares consisting of morphisms in form the desired independence relation. This generalizes the category-theoretic construction of stable independence relations using effective unions or cellular squares by M. Lieberman, S. Vasey and the second author to the unstable setting.
33 pages