Vol. 4, No. 1, 2022

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Homotopy theory of equivariant operads with fixed colors

Peter Bonventre and Luís A. Pereira

Vol. 4 (2022), No. 1, 87–158
DOI: 10.2140/tunis.2022.4.87
Abstract

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

Keywords
operads, equivariant, homotopy theory, colored operads, model categories
Mathematical Subject Classification
Primary: 18M75, 18N40
Secondary: 55P48
Milestones
Received: 3 November 2020
Revised: 7 June 2021
Accepted: 7 July 2021
Published: 30 March 2022
Authors
Peter Bonventre
Department of Mathematics & Statistics
Georgetown University
Washington, DC
United States
Luís A. Pereira
Physics Building
Duke University
Durham, NC
United States