Definition. Underlying multicategory of a monoidal category [mde-R0DS]

Given an (unbiased) monoidal category \(M\), define the underlying multicategory \(\bar {M}\) to have objects those of \(M\) and multimorphisms,

\[\bar {M}(A_1, ..., A_n; A) := M(A_1 \otimes ... \otimes A_n; A).\]

Composition and identities are inherited from \(M\).

For biased monoidal categories, the underlying monoidal category is unique up to unique isomorphism (Elmendorf 2023).