On higher monoidal $\infty$-categories

Abstract

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 ${\mathbf{O}}_{\mathrm{rev}}$-monoidal $\infty$-categories and left adjoint oplax ${\mathbf{O}}_{\mathrm{rev}}$-monoidal functors, where ${\mathbf{O}}_{\mathrm{rev}}^{\otimes }$ is a sequence obtained by reversing the order of ${\mathbf{O}}^{\otimes }$.

18 pages

References in corpus (1)

• Hopf comonads on naturally Frobenius map-monoidales