• If there exists a natural transformation
    \[ \alpha ^{\boxtimes }_{A,B,C}\colon \webleft (A\boxtimes _{\mathcal{C}}B\webright )\otimes _{\mathcal{C}}C\to A\boxtimes _{\mathcal{C}}\webleft (B\otimes _{\mathcal{C}}C\webright ) \]

    making the diagrams

    and

    commute, then the natural transformation $\text{id}^{\otimes }$ satisfies the monoidality condition of Item 2 of Remark 10.1.1.1.3.


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