On the homotopy theory of equivariant colored operads

Bonventre, Peter; Pereira, Luís A

doi:10.2140/agt.2022.22.2631

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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

Volume 22, issue 6 (2022)