Natural Transformation = Data Migration
A natural transformation $\eta: F \Rightarrow G$ maps data:
$\eta_{\text{Person}}$: identity on people
$\eta_{\text{City}}$: identity on cities
But updates how $lives_in$ points
This satisfies the naturality condition:
$G(lives_in) \circ \eta_{\text{Person}} = \eta_{\text{City}} \circ F(lives_in)$
So the structure (foreign key logic) is preserved even after the data update.