In case anyone still thinks that these two Jacobi rules are distinct, let us recall the antisymmetry rule for the braid diagram.
We observe that the correct $t$ channel diagram is recovered, so that the terms of the Jacobi identity are rearranged to the correct form. Seeing that modern QCD hinges on laws from braided monoidal categories gives us hope that we can understand their generalisations to non perturbative methods for gravity. Note also that there is a right handed braided Jacobi rule, obtained as usual by reflection of the diagram.
6 years ago