Effective colimits

Let \(T\) be a category with pullbacks and \(I\)-indexed colimits. We say that \(I\)-indexed colimits in \(T\) are effective if, for every cartesian transformation \(Y_{\bullet} \to X_{\bullet}\) of functors \(I \to T\), the extended natural transformation \(\overline{Y}_{\bullet} \to \overline{X}_{\bullet}\) of colimit cocones \(I^{\triangleright} \to T\) is again cartesian, i.e. for every \(j \in I\) the commutative square

is a pullback square.