Global homotopy theory via spectral Mackey functors

TL;DR

This paper establishes an equivalence between Hausmann's global stable homotopy theory model and spectral Mackey functors, providing a new categorical perspective and extending to ultra-commutative monoids.

Contribution

It introduces an equivalence between global stable homotopy theory and spectral Mackey functors, and describes ultra-commutative monoids as space-valued global Mackey functors.

Findings

Equivalence between Hausmann's model and spectral Mackey functors.

Description of ultra-commutative monoids as space-valued global Mackey functors.

Framework connecting global homotopy theory with spectral Mackey functors.

Abstract

We show that Hausmann's model of global stable homotopy theory in terms of symmetric spectra is equivalent to the $\infty$-category of spectral Mackey functors in the sense of Barwick on a certain global effective Burnside category. We moreover provide an analogous description of Schwede's ultra-commutative monoids as space-valued global Mackey functors.