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

Peter Bonventre and Luís A Pereira

Algebraic & Geometric Topology 20 (2020) 2687–2778
DOI: 10.2140/agt.2020.20.2687
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–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.

Keywords
operads, dendroidal sets, preoperads, equivariant homotopy theory, Reedy categories
Mathematical Subject Classification 2010
Primary: 55U10, 55U35, 55U40
Secondary: 18G30
References
Publication
Received: 21 January 2018
Revised: 14 October 2019
Accepted: 26 October 2019
Published: 8 December 2020
Authors
Peter Bonventre
Department of Mathematics
University of Kentucky
Lexington, KY
United States
Luís A Pereira
Department of Mathematics
Duke University
Durham, NC
United States