ScalingStacks

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