This paper considers the possible underlying multicategories for a symmetric monoidal category, and shows that, up to canonical and coherent isomorphism, there really is only one. As a result, there is a well-defined forgetful functor from symmetric monoidal categories to multicategories, as long as all morphisms of symmetric monoidal categories are at least lax symmetric monoidal.
Keywords: symmetric monoidal category, multicategory
2020 MSC: 18M05
Theory and Applications of Categories, Vol. 44, 2025, No. 29, pp 869-926.
Published 2025-09-17.
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