Lifting independence along functors

Abstract

Given a functor $F:\mathcal{C}\to \mathcal{D}$ and a model-theoretic independence relation on $\mathcal{D}$, we can lift that independence relation along $F$ to $\mathcal{C}$ by declaring a commuting square in $\mathcal{C}$ to be independent if its image under $F$ is independent. For each property that an independence relation can have we give assumptions on the functor that guarantee the property to be lifted.

38 pages

References in corpus (9)

• Canonical forking in AECs
• Building independence relations in abstract elementary classes
• Forking independence from the categorical point of view
• Existentially Closed Exponential Fields
• The Kim-Pillay theorem for Abstract Elementary Categories
• Bilinear spaces over a fixed field are simple unstable
• NSOP${}_1$-like independence in AECats
• Independence relations for exponential fields
• Unstable independence from the categorical point of view