Theorem A. (proposition 6.4.2).
There is a monoidal \((\infty,2)\)-category \({\mathbf K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) with objects labelled by natural numbers \(n \in \mathbb{N}_0\) and whose endomorphim \(\infty\)-categories are the \(k\)-linear, stable, idempotent-complete \(\infty\)-categories \({\mathbf K}^b(\mathrm{Sbim}_n)\) of chain complexes of Soergel bimodules, with a \(\mathbb{Z}\)-action by grading shift. More precisely, \({\mathbf K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) defines an \(\mathbb E_1\)-algebra in the symmetric monoidal \(\infty\)-category \(\mathrm{Cat}[\mathrm{st}^{B\mathbb{Z}}_{k}]\).