I'm having trouble understanding the following proof from Joyal and Street's paper Braided Monoidal Categories.
B1 and B2 are the hexagon axioms:
To get a triangular diagram starting from a hexagon diagram, it seems like the associators are getting removed somehow (by using the identity triangle axioms of monoidal categories? not sure). I'm new to this and I'm having trouble figuring out exactly how the proof works. I'd appreciate it if someone could provide the actual details.
To solve it, you need to show that given the Hexagonal equation $B1$, you can somehow build $B3$ and $B4$ insides $B1$. And since the outer diagram $B1$ commutes and some of the inside diagrams because of the monoidal structure of category commutes, then $B3$ and $B4$ commute. Please find below a proof sketch.