Coherence in Substructural Categories

Details Coherence in Substructural Categories Coherence in Substructural Categories

2000-06-08

arxiv.org/abs/math/0006061v1

Mathematics

Category Theory

19 pages

Scientific paper

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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