The coalgebraic enrichment of algebras in higher categories

Abstract

We prove that given C a presentably symmetric monoidal ∞-category, and any essentially small ∞-operad O , the ∞-category of O -algebras in C is enriched, tensored and cotensored over the presentably symmetric monoidal ∞-category of O -coalgebras in C . We provide a higher categorical analogue of the universal measuring coalgebra. For categories in the usual sense, the result was proved by Hyland, López Franco, and Vasilakopoulou.