Is there a nice/unique way to express the pseudofunctor laws (<http://ncatlab.org/nlab/show/pseudofunctor>) when you don't have horizontal composition, only whiskering? I don't want to define horizontal composition because it's only unique up to homotopy, as per the argument in [chapter 9 of the HoTT book](http://books.google.nl/books?id=LkDUKMv3yp0C&hl=en&printsec=frontcover&pg=PA306&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false).



Expressing the pseudofunctor laws uniquely with whiskering rather than horizontal composition?
I did not realize that all the horizontal compositions listed on the [nlab page](http://ncatlab.org/nlab/show/pseudofunctor) had the identity on one side or the other. Since whiskering is equivalent to horizontal composition with the identity, it's easy to rephrase all the horizontal compositions as whiskerings.


