  We show that for the path algebra $A$ of an acyclic quiver, the singularity
category of the derived category $\mathsf{D}^{\rm b}(\mathsf{mod}\,A)$ is
triangle equivalent to the derived category of the functor category of
$\underline{\mathsf{mod}}\,A$, that is, $\mathsf{D}_{\rm sg}(\mathsf{D}^{\rm
b}(\mathsf{mod}\,A))\simeq \mathsf{D}^{\rm
b}(\mathsf{mod}(\underline{\mathsf{mod}}\,A))$. This extends a result of
Iyama-Oppermann for the path algebra $A$ of a Dynkin quiver. An important step
is to establish a functor category analog of Happel's triangle equivalence for
repetitive algebras.
