Definition 2.3.
Given two functors \(F,G\colon I \to T\), a natural transformation \(\alpha\colon F \to G\) is called cartesian if for every morphism \(i \to j\) in \(I\) the naturality square
is a pullback square. We denote by \(\Fun^{\cart}(I,T) \subseteq \Fun(I,T)\) the wide subcategory spanned by the cartesian natural transformations.