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On the homotopy theory of equivariant colored operads

Peter Bonventre and Luís A Pereira

Algebraic & Geometric Topology 22 (2022) 2631–2688
DOI: 10.2140/agt.2022.22.2631
Abstract

We build model structures on the category of equivariant simplicial operads with weak equivalences determined by families of subgroups, in the context of operads with a varying set of colors (and building on the fixed color model structures in the prequel). In particular, by specifying to the family of graph subgroups (or, more generally, one of the indexing systems of Blumberg–Hill), we obtain model structures on the category of equivariant simplicial operads whose weak equivalences are determined by norm map data.

Keywords
operads, model categories, colored operads, equivariant operads, equivariant homotopy theory, simplicial operads
Mathematical Subject Classification
Primary: 55U10, 55U35, 55U40
References
Publication
Received: 4 April 2020
Revised: 23 February 2021
Accepted: 23 July 2021
Published: 13 December 2022
Authors
Peter Bonventre
College of the Holy Cross
Worcester, MA
United States
Luís A Pereira
Duke University
Durham, NC
United States