Please clarify the meaning of $\text{End}_R(R_R, R_R) \cong R$

Question

First of all, I have no idea what $\text{End}_R(R_R, R_R) \cong R$ is even supposed to mean. The $R$ in $\text{End}_R$ is supposed to be a category, but the $R$ in $R_R$ is an object in that category. So I don't even know what the question is asking.

Answer 1

I agree with hardmath's comment that notation should be referenced in context, but here's my best guess.

$R$ is a ring. $R_R$ is a notation for the ring $R$, considered as a module over itself (i.e., as an object in the category $R-\textbf{mod}$). $\mathrm{End}_R$ refers the endomorphism ring of endomorphisms in the category $R-\textbf{mod}$; i.e., the $R$ subscript in $\mathrm{End}_R$ is short for $R-\textbf{mod}$. As the endomorphism ring and $R$ are both rings, the isomorphism in question in as isomorphism of rings.