Equivariant dendroidal Segal spaces and \(G\)-\(\infty\)-operads (Q2663383)

In a series of three papers, Cisinski and Moerdijk developed and gave comparisons for several different models for infinity operads. The present paper, part of a larger project by the two authors, generalizes the second of these [\textit{D.-C. Cisinski} and \textit{I. Moerdijk}, J. Topol. 6, No. 3, 675--704 (2013; Zbl 1291.55004)] to the genuine equivariant setting. The aim of the project as a whole is to show there is a right Quillen equivalence, the homotopy coherent nerve, going from a model category of equivariant simplicial operads to a model structure for `\(G\)-\(\infty\)-operads.' The types of infinity operads considered are not simply \(G\)-equivariant (for a finite group \(G\)), but also encode certain norm maps, as appear for instance in [\textit{A. J. Blumberg} and \textit{M. A. Hill}, Adv. Math. 285, 658--708 (2015; Zbl 1329.55012)]. This additional complication does not arise in the categorical case from [\textit{J. E. Bergner}, Glasg. Math. J. 59, No. 1, 237--253 (2017; Zbl 1380.55015)]. The main constructions of the paper are model structures for complete equivariant dendroidal Segal spaces and equivariant Segal operads. There is a Quillen equivalence between these, and also a Quillen equivalence between the complete equivariant dendroidal Segal space model and the model structure for \(G\)-\(\infty\)-operads from [\textit{L. A. Pereira}, Algebr. Geom. Topol. 18, No. 4, 2179--2244 (2018; Zbl 1392.55017)]. The authors also indicate how the results generalize to arbitrary Blumberg-Hill indexing systems. Further, they provide an appendix dedicated to an equivariant version of the generalized Reedy categories of [\textit{C. Berger} and \textit{I. Moerdijk}, Math. Z. 269, No. 3--4, 977--1004 (2011; Zbl 1244.18017)].