Homotopy theory of equivariant operads with fixed colors

TL;DR

This paper develops model structures for equivariant simplicial operads with fixed colors, using subgroup families to define weak equivalences, advancing the understanding of equivariant operad homotopy theory.

Contribution

It introduces new model structures on equivariant operads with fixed colors based on subgroup families, including graph subgroups and indexing systems, incorporating norm map data.

Findings

Established model structures for equivariant operads with fixed colors.

Connected subgroup families to weak equivalences in the model structures.

Extended the framework to include norm map data via specific subgroup families.

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-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.