M Theory Lesson 157
What might this mean for mutually unbiased bases? Instead of bases we can consider $d$ change of basis maps for a prime $d$ dimensional space. Instead of being ordinary matrices, these operators are permitted to be less well defined under a tensor product, via the tensorator. For example, if $f \otimes g$ is only defined up to a scalar, depending on the order of composition, the map $\phi$ might correspond to multiplication by the scalar between the two alternative types of $f \otimes g$. Thus higher categories offer excellent ways of cheating to get just what one wants!
Aside: What is Category Theory? is a lovely book, which one can browse with Google. It contains a helpful article by Coecke: Introducing categories to the practicing physicist.