I seem to recall that there was some difficulty for the coherence of lax and oplax monoidal functors (properly so called, meaning with unit maps in addition to the natural transformation). Epstein's 1966 paper handles what I would call symmetric semigroupal functors (symmetry, but no units), and his proof goes through without the symmetry. I have also once as an exercise prove the coherence theorem for strong monoidal functors. This query arises tangentially in regard to a paper I am writing on the deformation theory of monoidal categories and functors. An answer is not strictly needed, but I'd be greatful for a reference to the difficulty, or a corrective to a mis-recollection on my part. (It would be nice to include in the paper.) Best Thoughts to all, David Yetter