Models of G-spectra as presheaves of spectra

TL;DR

This paper develops new models for G-spectra using categories of functors to spectra, simplifying the understanding of equivariant stable homotopy theory through categorical and topological approaches.

Contribution

It introduces explicit Quillen equivalent models for G-spectra as categories of spectrally enriched functors, utilizing equivariant infinite loop space theory and Atiyah duality.

Findings

Models are Quillen equivalent to the category of G-spectra.

Recasts equivariant stable homotopy theory in categorical terms.

Provides topologically grounded models based on Atiyah duality.

Abstract

Let G be a finite group. We give Quillen equivalent models for the category of G-spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data. It recasts equivariant stable homotopy theory in terms of point-set level categories of G-spans and nonequivariant spectra. We also give a more topologically grounded model based on equivariant Atiyah duality.