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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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