∞-OPERADS AS SYMMETRIC MONOIDAL ∞-CATEGORIES

We use Lurie's symmetric monoidal envelope functor to give two new descriptions of oo-operads: as certain symmetric monoidal oo-categories whose underlying symmetric monoidal oo-groupoids are free, and as certain symmetric monoidal oo-categories equipped with a symmetric monoidal functor to finite sets (with disjoint union as tensor product). The latter leads to a third description of oo-operads, as a localization of a presheaf oo-category, and we use this to give a simple proof of the equivalence between Lurie's and Barwick's models for oo-operads.