Lifting independence along functors

Ji\v{r}\'i Rosick\'y; Mark Kamsma

arxiv: 2411.14813 · v2 · pith:L2HY2PZHnew · submitted 2024-11-22 · 🧮 math.CT · math.LO

Lifting independence along functors

Mark Kamsma , Ji\v{r}\'i Rosick\'y This is my paper

classification 🧮 math.CT math.LO

keywords mathcalindependencerelationalongfunctorindependentpropertyassumptions

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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.

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