ScalingStacks

Assume that \(\mathcal C\) contains a terminal object. Then, there exists a left adjoint to the fully faithful inclusion, which is given by the formula \(c \mapsto \mathrm{Fact}(c \rightarrow{\sf pt}_\mathcal C)\). Moreover, the right adjoint is the inclusion of the \(\mathcal L\)-local objects, and hence the left adjoint exhibits \(\mathcal C^\mathcal R\) as the localization \(\mathcal C[\mathcal L^{-1}]\).⁷⁰