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Coherence in Substructural Categories

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Abstract

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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  1. Mathematical Institute, Knez Mihailova 35, P.O. Box 367, 11001, Belgrade, Yugoslavia

    Zoran Petrić

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  1. Zoran Petrić
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Petrić, Z. Coherence in Substructural Categories. Studia Logica 70, 271–296 (2002). https://doi.org/10.1023/A:1015186718090

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