It follows from example 8.1.2 that for an ordinary braided monoidal \(1\)-category \(\mathcal C\), and monoidal \(1\)-functors \(\mathcal A\xrightarrow{F} \mathcal B\xrightarrow{g} \mathcal C\) between ordinary monoidal \(1\)-category, the space \(\mathrm{PreBraid}_{\mathrm{Cat}_{({1}, {1})}}(F)_{/C}\) of prebraidings on \(F\) over \(C\) in the sense of definition 8.1.4 agrees with the set \(\mathrm{PreBraid}_{/C}(F)\) of prebraidings over \(C\) from definition 2.4.8.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2