The homotopy \(1\)-category \(h_1{\mathbf K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) of the monoidal \((\infty,2)\)-category \({\mathbf K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) agrees with the monoidal \(1\)-category \(h_1\mathrm{K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) from definition 2.3.2.
Moreover, after taking homotopy \(1\)-categories, the monoidal \((\infty,2)\)-functor \(\mathrm{BSbim}\rightarrow\mathrm{Sbim}\rightarrow{\mathbf K}^b_{\mathrm{loc}}(\mathrm{Sbim})\) becomes the ordinary monoidal \(1\)-functor \[h_1 \mathrm{BSbim}\rightarrow h_1 \mathrm{K}^b_{\mathrm{loc}}(\mathrm{Sbim})\] from ([001D]).