ScalingStacks

definition 4.5.7 defines a large symmetric monoidal \(\mathrm{st}_{Hk}^{BZ}\)-enriched \(\infty\)-category \[\mathrm{DMor}^{\mathrm{flat}, \mathrm{gr-perf}}(\mathrm{mod}_{k}^{Z})\in \mathrm{CAlg}(\widehat{\mathrm{Cat}}[\mathrm{st}_{Hk}^{BZ}])\] equipped with a symmetric monoidal surjective-on-objects functor \[\mathrm{Alg}(\mathrm{mod}_k^{Z, \mathrm{flat}}) \rightarrow\mathrm{DMor}^{\mathrm{flat}, \mathrm{gr-perf}}(\mathrm{mod}_{k}^{Z}).\] The stable \(k\)-linear hom-category between algebras \(A, B \in \mathrm{Alg}(\mathrm{mod}_k^{Z, \mathrm{flat}})\) is \(\mathcal D(_A\mathrm{grbmod}_B)^{\mathrm{gr-perf}}\) with \(Z\)-action by grading shift.