I just found some nice slides on Mac Lane's coherence theorem, which says _roughly_ that all diagrams built using tensor products, the unit object, associators and unitors in a monoidal category commute:

* Peter Hines, [Reconsidering MacLane:the foundations of categorical coherence](http://www-users.york.ac.uk/~varg1/MATHS1.pdf), October 2013.

It goes into a lot of the subtleties... which is good if the subtleties matter to you.

I'll add this reference to the lecture.