ScalingStacks

The composite \[ (-)^{\mathrm{fin}} \colon \mathrm{add}\xrightarrow{\mathcal P^{\Sigma}} \mathrm{Pr}^{\mathrm{L}, \mathrm{cp}}_{\mathrm{add}}\xrightarrow{\mathrm{Const.}~\href{/tag/0058}{3.4.4}} \mathrm{Pr}^{\mathrm{L}, \mathrm{c}}_{\mathrm{st}}\xrightarrow{(-)^{\mathrm{c}}} \mathrm{st}\] defines a morphism in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\) which is the left adjoint to the forgetful functor \(\mathrm{st}\rightarrow\mathrm{add}\).
For \(\mathcal C\in \mathrm{add}\), the unit \(\mathcal C\rightarrow\mathcal C^{\mathrm{fin}}\) of the adjunction is a fully faithful additive functor.