Given a functor \(F: \mathcal {C}\rightarrow \mathcal {D}\) 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 of interest that an independence relation can have we give assumptions on the functor that guarantee the property to be lifted.
