Reading advice

Concerning the question by Lindquist: The tensor product automatically satisfies all functoriality, associativity and coherence conditions, if it is introduced by a universal property as by Bourbaki. This is shown for monoidal categories (bicategories with one object) e.g. in my paper ``Multicategories revisited'', Contemporary Mathematics 92(1989). The same argument works for arbitrary bicategories provided, in defining a multicategory, one replaces the free monoid generated by a set by the free category generated by a graph. Jim Lambek