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Are there any references for model categorical presentations of the $(\infty,1)$ category of (not necessarily symmetric) monoidal $\infty$-categories?

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Example 4.1.4.7 in Lurie's Higher Algebra shows that the underlying quasicategory of the model category of monoids in marked simplicial sets is equivalent to the quasicategory of small symmetric monoidal ∞-categories.

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