  In this paper we introduce a notion of $\mathbf{O}$-monoidal
$\infty$-categories for a finite sequence $\mathbf{O}^{\otimes}$ of
$\infty$-operads, which is a generalization of the notion of higher monoidal
categories in the setting of $\infty$-categories. We show that the
$\infty$-category of coCartesian $\mathbf{O}$-monoidal $\infty$-categories and
right adjoint lax $\mathbf{O}$-monoidal functors is equivalent to the opposite
of the $\infty$-category of Cartesian $\mathbf{O}_{\rm rev}$-monoidal
$\infty$-categories and left adjoint oplax $\mathbf{O}_{\rm rev}$-monoidal
functors, where $\mathbf{O}^{\otimes}_{\rm rev}$ is a sequence obtained by
reversing the order of $\mathbf{O}^{\otimes}$.
