Multiplicative structures on comodules in higher categories

Abstract

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