ScalingStacks

Fix a morphism \(\mathcal A\rightarrow\mathcal B\) in \(\mathrm{Op}_{/\mathcal O}\). Then, in the adjunction we have \(F_\mathcal A^\mathcal B(\mathcal L_\mathcal A) \subseteq \mathcal L_\mathcal B\) and \(U_\mathcal A^\mathcal B(\mathcal R_\mathcal B) \subseteq \mathcal R_\mathcal A\) (using the notation of part ([00L4])). In particular, the factorization systems of part ([00L4]) determine a lift through the indicated forgetful functor.