ScalingStacks

Remark 4.2.3. It is not difficult to show that $\tau_{\leq d}$ extends to a functor from the $\infty$-category of presentable $\infty$-categories to the full subcategory spanned by presentable essentially $\left(d+1\right)$-categories and that it is left adjoint to the inclusion. The maps $\tau_{\leq d}^{\mathcal{C}}$ can be taken to be the components of the unit transformation (this essentially follows from T.5.5.6.22), but we shall not need this.