Re: Units in lax and oplax monoidal functors

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).

For the lax case, see Geoffrey Lewis, Coherence for a closed functor, LNM 281 (Springer, 1972) 148-195. For coherence of strong monoidal (= tensor preserving) functors, see A. Joyal and R. Street, Braided tensor categories, Advances in Math 102 (1993) 20-78; MR94m:18008. Best wishes, Ross