Universal colimits

Let \(T\) be a category with pullbacks and \(I\)-indexed colimits. We say that \(I\)-indexed colimits in \(T\) are universal if, for every morphism \(f\colon A \to B\), the pullback functor \(f^*\colon T_{/B} \to T_{/A}\) preserves \(I\)-indexed colimits.