Mackey functors from the viewpoint of double category theories

Abstract

Let $G$ be a finite group. In this paper, we first introduce a new notion, so-called the Mackey double category of $G$. Then we prove that the category of Mackey double categories and the category of Mackey functors of $G$ are equivalent.

There are some problems with the definition of Mackey double categories (Section 3.1)