Module as a functor

Question

A left $R$-module is said to be a covariant functor from the category with one object $R$ to the category of abelian groups. Is this $R$ considered as a ring or as or as a left $R$ module? I am only able to interpret it as the latter since a module is given by a homomorphism from $R$ to $End(M)$, where $M$ is an abelian group. And $R$ as a ring is isomorphic to $End(R)$ where $R$ is viewed as a left module. But in the texts it's not stated that they consider that single object to be a module, so I assume I'm wrong.