Constructing equivariant spectra via categorical Mackey functors

TL;DR

This paper presents a new categorical method to construct equivariant spectra from Mackey functors, utilizing recent advances in the description of equivariant spectra and K-theory, with applications to Eilenberg--MacLane spectra and G-set suspension spectra.

Contribution

It introduces a functorial construction of equivariant spectra from generalized Mackey functors using spectrally-enriched categories and K-theory, expanding the toolkit for equivariant stable homotopy theory.

Findings

Constructs equivariant spectra functorially from Mackey functors.

Provides new models for equivariant Eilenberg--MacLane spectra.

Develops functorial suspension spectra for finite G-sets.

Abstract

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key element of our construction is a spectrally-enriched functor from a spectrally-enriched version of permutative categories to the category of spectra that is built using an appropriate version of K-theory. As applications of our general construction, we produce a new functorial construction of equivariant Eilenberg--MacLane spectra for Mackey functors and for suspension spectra for finite G-sets.