A bicategorical analysis of E-categories

coherence theorem for bicategories) Every bicategory is biequivalent to a 2-category. Proof This is immediate from the existence of Yoneda pseudo-functor. First note that the codomain Bicat(B op ; Cat) of Yoneda pseudo-functor Y is a 2-category, since Cat is so. Take the full sub-2-category R of the pseudofunctor 2-category Bicat(B op ; Cat) consisting of representable pseudo-functors, and regard the codomain of Y to be R. The pseudo-functor thus defined is still full and faithful, and every object of R is equivalent to an image under Y by the very definition of R. So, Y is a biequivalence from B to R. [] The Theorem 4.1 states almost all of what the coherence theorem says. In fact, it is treated as an alternative way to state the coherence theorem for bicategories in [4]. However, the road from Theorem 4.1 to the coherence theorem for bicategories still contains some delicate part. So, we explicitly state the full argument here. In the sequel, let B be a bicategory with tenso..