Enriched infinity-operads

In the last talk I introduced dendroidal sets as a useful model for $\infty$-operads which can be viewed as operads enriched in spaces. By working with ordinary operads, one often realizes that many interesting operads such as the operads for Lie algebras, Poisson algebras and Gerstenhaber algebras are not enriched in topological spaces but over vector spaces or - more generally - in chain complexes. If we want to define and study the $\infty$-categorical version of these algebras, we need a theory of enriched $\infty$-operads in advance.

 

In this talk I will introduce $\infty$-operads which are enriched in an arbitrary symmetric monoidal $\infty$-category. In particular, I will present an enriched version of dendroidal sets and compare it with other models for enriched $\infty$-operads.