We leave it to the reader to check that the involved categories are monoidal as claimed. The conceptual reason behind this is that these categories are the shadow of monoidal bicategories in the sense of [Bén67] (the objects are the same, but morphism categories are given for instance by \(\mathrm{K}^b(\mathrm{Sbim}_n)\) instead of the sets \(h_0 \mathrm{K}^b(\mathrm{Sbim}_n)\) in ([001C])). Although these monoidal bicategories play an important conceptual role in represention theory and quantum topology, see e.g. [EW16, HRW21, HRW21], the construction of the monoidal structure has not yet appeared in full detail in the literature. In the world of \(\infty\)-categories we will obtain an analogous construction in section 6.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2