We define the monoidal functor \[ h_1 H_{\mathrm{loc}}\colon h_1 \mathrm{K}^b_{\mathrm{loc}}(\mathrm{Sbim}) \rightarrow h_1\mathrm{DMor}^{\mathrm{poly}, \mathrm{gr-perf}}(\mathrm{mod}_k^{\mathbb{Z}}),\] which takes an object \(n\) to the polynomial algebra \(R_n\) and a chain homotopy equivalence class of a chain complex of Soergel bimodules to the corresponding quasi-isomorphism class of complexes of graded bimodules.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2