Constructing equivariant spectra via categorical Mackey functors

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–Mac Lane spectra for Mackey functors and for suspension spectra for finite $G$–sets.