Unstable independence from the categorical point of view

Abstract

We give a category-theoretic construction of simple and NSOP${}_1$-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 $\mathcal{M}$ such that the pullback squares consisting of morphisms in $\mathcal{M}$ 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.

arXiv comment33 pages

References in corpus (8)

• Sheafifiable homotopy model categories
• Canonical forking in AECs
• Generic expansion and Skolemization in NSOP${}_1$ theories
• Forking independence from the categorical point of view
• Universal abstract elementary classes and locally multipresentable categories
• The Kim-Pillay theorem for Abstract Elementary Categories
• Bilinear spaces over a fixed field are simple unstable
• NSOP${}_1$-like independence in AECats

Cited by in corpus (1)

• Lifting independence along functors