We prove that given $\mathcal{ C}$ a presentably symmetric monoidal $\infty$-category, and any essentially small $\infty$-operad $\mathcal{ O}$, the $\infty$-category of $\mathcal{ O}$-algebras in $\mathcal{ C}$ is enriched, tensored and cotensored over the presentably symmetric monoidal $\infty$-category of $\mathcal{ O}$-coalgebras in $\mathcal{ C}$. We provide a higher categorical analogue of the universal measuring coalgebra. For categories in the usual sense, the result was proved by Hyland, L\'{ o}pez Franco, and Vasilakopoulou.
Categories: math.AT math.CT