Hinich's model for Day convolution revisited

Abstract

We prove that Hinich's construction of the Day convolution operad of two $\mathcal{O}$-monoidal $\infty$-categories is an exponential in the $\infty$-category of $\infty$-operads over $\mathcal{O}$, and use this to give an explicit description of the formation of algebras in the Day convolution operad as a bivariant functor.