∞ -Operads via symmetric sequences

Abstract

We construct a generalization of the Day convolution tensor product of presheaves that works for certain double \infty -categories. Using this construction, we obtain an \infty -categorical version of the well-known description of (one-object) operads as associative algebras in symmetric sequences; more generally, we show that (enriched) \infty -operads with varying spaces of objects can be described as associative algebras in a double \infty -category of symmetric collections.