As defined, \(\mathrm{BSbim}_n\) is a monoidal full subcategory of the \(k\)-linear category of graded \(R_n\)-bimodules and grading-preserving bimodule maps, with tensor product \(-\otimes_{R_n}-\). More precisely, since each \(B_i\) is free of rank \(2\) as a graded \(R_n\)-module from the left and from the right, all objects of \(\mathrm{BSbim}_n\) are finitely generated graded-projective12 \(R_n\)-modules from both sides and the tensor product coincides with the derived tensor product.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2