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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeOct 19th 2021

### Free rigid monoidal categories

The inclusion of the 2-category of monoidal categories into the 2-category of rigid monoidal categories admits a left 2-adjoint functor $L$.

Furthermore, the unit of the adjunction is a strong monoidal fully faithful functor, i.e., any monoidal category $C$ admits a fully faithful strong monoidal functor $C\to L(C)$, where $L(C)$ is a rigid monoidal category.

See Theorems 1 and 2 in Delpeuch \cite{Delpeuch}.