makeBurnsideMackeyFunctor -- constructs the Burnside Mackey functor

The Burnside Mackey functor of a group $G$ is defined by sending $G/H$ to the Burnside ring $A(H)$, with transfer and restriction coming from transfer and restriction of finite $G$-sets. When $G$ is a cyclic group of prime order, these maps admit a particularly nice form. The underlying module is given by $\mathbb{Z}$, with trivial conjugation action, while the fixed module is $\mathbb{Z}\{1,t\}$. Restriction is defined as $$\text{res}_e^{C_p} \colon \mathbb{Z}\{1,t\} \to \mathbb{Z}$$ by sending $t\mapsto p$. Transfer is of the form $$\text{tr}_e^{C_p} \colon \mathbb{Z} \to \mathbb{Z}\{1,t\}$$ by sending $x\mapsto xt$.