Group actions on Segal operads

TL;DR

This paper establishes a Quillen equivalence linking simplicial operads and Segal operads, and extends this to include group actions, bridging different models of operadic structures.

Contribution

It introduces a Quillen equivalence between model structures for simplicial operads and Segal operads, including those with group actions, advancing the understanding of operad models.

Findings

Established a Quillen equivalence between simplicial and Segal operads.

Extended the equivalence to operads with group actions.

Bridged different frameworks for modeling operadic structures.

Abstract

We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spaces. We then extend this result to give an Quillen equivalence between the model structures for simplicial operads equipped with a group action and the corresponding Segal operads.