Lifting independence along functors

TL;DR

This paper explores how to transfer model-theoretic independence relations along functors between categories, providing conditions under which properties of independence are preserved during the transfer.

Contribution

It introduces a method for lifting independence relations along functors and establishes conditions for preserving various independence properties.

Findings

Provides a framework for lifting independence relations along functors.

Identifies assumptions on functors that preserve independence properties.

Enables transfer of model-theoretic independence concepts across categories.

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.