Equivariant dendroidal Segal spaces and $G$-$\infty$-operads

Abstract

We introduce the analogues of the notions of complete Segal space and of Segal category in the context of equivariant operads with norm maps, and build model categories with these as the fibrant objects. We then show that these model categories are Quillen equivalent to each other and to the model category for $G$-$\infty$-operads built in a previous paper. Moreover, we establish variants of these results for the Blumberg-Hill indexing systems. In an appendix, we discuss Reedy categories in the equivariant context.