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Description

We introduce enriched $\infty$-operads as certain presheaves which generalize Barwick's complete Segal operads. The simple structure of the indexing categories allows us to define algebras between enriched $\infty$-operads. By comparing this presheaf model with an enriched version of Moerdijk-Cisinski's dendroidal Segal spaces, we then prove a rectification theorem which states that the homotopy theory of $\infty$-operads enriched in a nice symmetric monoidal model category is equivalent to that of strictly enriched operads. From this we can easily infer that all established models for $\infty$-operads are equivalent to simplicially enriched operads. The talk is based on joint work with Rune Haugseng.