ScalingStacks

Recall from ([00CP]) the adjunction where the right adjoint forgets additivity, \(k\)-linearity and the \(\mathbb{Z}\)-action and the (strongly) symmetric monoidal left adjoint \(\mathrm{Lin}_{k, \mathrm{loc}}^{\mathbb{Z}} (-)\) sends an \((\infty,2)\)-category \(\mathcal C\) to the locally additive \(k\)-linear \((\infty,2)\)-category with local shifts with the same objects as \(\mathcal C\) and hom-categories given by the linearization \(\mathrm{Lin}_k(\underline{\mathrm{Hom}}_{\mathcal C}(a,b) \times \mathbb{Z})\) with free \(\mathbb{Z}\)-action.