I'm trying to understand more explicitly what the natural homomorphism is for an $R$-module $M$ to the dual of it's dual $(M^\ast)^\ast$.
It makes sense to compose the natural homomorphism twice by $ M\stackrel{\phi}{\to} M^*\stackrel{\psi}{\to} (M^*)^* $ and then just say the natural homomorphism is $\psi\circ\phi$. But what explicitly is $\phi$? To each $m\in M$, to what $f\in H^*$ do we associate it with?