So many times it’s necessary to ‘identify’ two more objects which are isomorphic, and the ‘canonical’ is supposed to justify why this doesn’t cause a problem.

So many times it’s necessary to ‘identify’ two more objects which are isomorphic, and the ‘canonical’ is supposed to justify why this doesn’t cause a problem. The reason it is necessary here is that the mapping D(f) -> A_f is a priori multi valued, and we need it to be single valued. However it’s fairly easy to make a definition which is trivially single valued , so I don’t think it’s a very instructive example of the phenomenon. Probably more pertinent is an n-fold tensor product with different bracket ordering