2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59375It 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.19 pagesCategory Theorytext