Let $G \subset SU(2)$ be a finite subgroup containing $-I$, and let $Q$ be the corresponding Euclidean graph. Given an orientation on $Q$, one can define the (bounded) derived category of the representations of the resulting quiver. Let $\bar{G} = G / {\pm I}$. Then one can also define the category $Coh_{\bar{G}}(\mathbb{P}^1)$ of $\bar{G}$-equivariant coherent sheaves on the projective line; this abelian category also has a (bounded) derived category. In the second of these talks dedicated to the McKay correspondence, we establish an equivalence between the two derived categories mentioned above.