ScalingStacks

The functor from corollary 4.4.5.([008R]) restricts to a symmetric monoidal \(\mathrm{add}_{Hk}^{BZ}\)-enriched functor \[\mathrm{Mor}^{\mathrm{flat}, \mathrm{gr-proj}}(\mathrm{mod}_{k}^{Z})\rightarrow\mathrm{DMor}^{\mathrm{flat}, \mathrm{gr-perf}}(\mathrm{mod}_{k}^{Z}).\] On objects this functor acts via the identity on \(\mathrm{Alg}(\mathrm{mod}_k^{Z, \mathrm{flat}})^{\simeq}\); on hom-categories between \(A, B \in \mathrm{Alg}(\mathrm{mod}_k^{Z, \mathrm{flat}})\) it is given by the additive \(k\)-linear \(Z\)-equivariant fully faithful inclusion \[_A\mathrm{grbmod}_B^{\mathrm{gr-cp}} \hookrightarrow \mathcal D(_A\mathrm{grbmod}_B)^{\mathrm{gr-perf}}.\]