Box Product of Mackey Functors in Terms of Modules

TL;DR

This paper describes the box product of Mackey functors using modules over the Mackey algebra, generalizing known results from cyclic p-groups to all finite groups.

Contribution

It provides a module-theoretic description of the box product of Mackey functors for any finite group, extending previous results from cyclic p-groups.

Findings

Recovered a known result for cyclic p-groups

Generalized the description to all finite groups

Connected Mackey functors with modules over the Mackey algebra

Abstract

The box product of Mackey functors has been studied extensively in Lewis's notes. As shown in Thevenaz and Webb's paper, a Mackey functor may be identified with a module over a certain algebra, called the Mackey algebra. We aim at describing the box product, in the sense of Mackey algebra modules. For a cyclic $p$-group $G$, we recover a result from Mazur's thesis. We generalize it to a general finite group $G$ in this article.