  We prove coherence theorems for bicategories, pseudofunctors and
pseudonatural transformations. These theorems boil down to proving the
coherence of some free $(4,2)$-categories. In the case of bicategories and
pseudofunctors, existing rewriting techniques based on Squier's Theorem allow
us to conclude. In the case of pseudonatural transformations this approach only
proves the coherence of part of the structure, and we use a new rewriting
result to conclude. To this end, we introduce the notions of white-categories
and partial coherence.
