Unstable independence from the categorical point of view

2023/10/24 by Mark Kamsma, Kamsma, Mark, Jiřı́ Rosický +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2310.15804

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a category-theoretic construction of simple and NSOP₁-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 M such that the pullback squares consisting of morphisms in M 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.

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