Proposition 6.2.5 (00CR) · ScalingStacks

The functor \(\mathrm{BSbim}\rightarrow\mathrm{Mor}^{\mathrm{poly}, \mathrm{gr-proj}}(\mathrm{mod}_k^{\mathbb{Z}})\) of monoidal \((\infty,2)\)-categories from corollary 6.1.3 factors through a monoidal \(\mathrm{add}_{k}^{B\mathbb{Z}}\)-enriched functor \[\mathrm{Lin}_{k, \mathrm{loc}}^{\mathbb{Z}} (\mathrm{BSbim}) \rightarrow\mathrm{Mor}^{\mathrm{poly}, \mathrm{gr-proj}}(\mathrm{mod}_k^{\mathbb{Z}}).\]

[00CS]

Proof.

Since \(\mathrm{Mor}^{\mathrm{poly}, \mathrm{gr-proj}}(\mathrm{mod}_k^{\mathbb{Z}})\) is an object in \(\mathrm{Alg}_{\mathbb E_1} (\mathrm{Cat}[\mathrm{add}_{k}^{B\mathbb{Z}}])\), the statement immediately follows from the adjunction ([00CQ]). ◻