Hinich's model for Day convolution revisited

We prove that Hinich’s construction of the Day convolution operad of two $\mathcal{O}$-monoidal $\mathrm{\infty }$-categories is an exponential in the $\mathrm{\infty }$-category of $\mathrm{\infty }$-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.