Theorem 2.5.2. (Prebraiding for Soergel bimodules).
The family of morphisms \(\beta_{m,n}\) from Definition 2.5.1 constitute a prebraiding on the functor \(h_1 K_{\mathrm{loc}}\colon h_1 \mathrm{BSbim}\rightarrow h_1 \mathrm{K}^b_{\mathrm{loc}}(\mathrm{Sbim})\).