  It is proved that MacLane's coherence results for monoidal and symmetric
monoidal categories can be extended to some other categories with
multiplication; namely, to relevant, affine and cartesian categories. All
results are formulated in terms of natural transformations equipped with
``graphs'' (g-natural transformations), and corresponding morphism theorems are
given as consequences. Using these results, some basic relations between the
free categories of these classes are obtained.
