Multiplicative structures on comodules in higher categories

In this paper we study multiplicative structures on comodules over bialgebras in the setting of $\mathrm{\infty }$-categories. We show that the $\mathrm{\infty }$-category of comodules over an $(\mathcal{O},\mathbf{A}\mathbf{s}\mathbf{s})$-bialgebra in a mixed $(\mathcal{O},\mathbf{A}\mathbf{s}\mathbf{s})$-duoidal $\mathrm{\infty }$-category has the structure of an $\mathcal{O}$-monoidal $\mathrm{\infty }$-category for any $\mathrm{\infty }$-operad $\mathcal{O}$.