Coherence in substructural categories

Studia Logica 70 (2):271 - 296 (2002)
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.
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