Box Product of $C_p$-Mackey Functors

Let $G$ be a finite group. In this paper, we begin by providing an exposition of $G$-Mackey functors and a symmetric monoidal product on the category of Mackey functors called the box product. After computing several examples of box products for the case of $G=C_p$, the cyclic group of order $p$, we move to the heart of the paper, which is to find and classify all $C_p$-Mackey functors invertible for the box product.