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Nov 1, 2010 at 9:49 comment added Zoran Skoda I suggest looking at B. Day, R. Street, Monoidal bicategories and Hopf algebroids, Advances in Mathematics, 129, 1 (1997) 99–157
Oct 30, 2010 at 16:29 comment added Justin Greenough Yes this is what I say. In the definition of monoidal category the associator is a natural isomorphism which therefore satisfies further naturality diagrams. The associator in the algebra-object case is simply a 2-cell which in general isn't required to satisfy anything like naturality. I wondered whether extra diagrams ought to have been included to reflect this, diagrams akin to those given in the paper of Kapranov and Voevodsky on quantum Yang-Baxter equations.
Oct 30, 2010 at 16:07 history answered Evan Jenkins CC BY-SA 2.5