2000/06/08 by Z. Petric, Petric, Z.
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #math.CT
paper · pdf · doi:10.48550/arxiv.math/0006061
19 pages
arxiv created 2000/06/08 · arxiv updated 2009/11/30
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.