${\mathcal{C}}$.

If $Q$ is an orientation of a simply-laced Dynkin diagram, then $ind({\mathcal{D}}^b({\mbox{{\rm mod \!}}}kQ))$ is equivalent to $k({\mathbb{Z}}Q)$.

### Example: type $A_n$ {#sect::typeA}

Many computations can be done easily in the derived category of a quiver of type $A_n$. Let $Q=1\to 2\to \ldots \to n$. Then $ind({\mathcal{D}}^b({\mbox{{\rm mod \!}}}kQ))$ is equivalent to the mesh category $k({\mathbb{Z}}Q)$, and so can be pictured as follows (for $n=4$): $${\footnotesize
   \xymatrix@!0{  &\begin{matrix} 1 \end{matrix}\ar[dr] && \begin{matrix} 2 \end{matrix}\ar[dr] && \begin{matrix} 3 \end{matrix}\ar[dr] && \begin{matrix} 4 \end{matrix}\ar[dr] && {\begin{matrix} 4\\ 3\\ 2\\ 1 \end{matrix}[1]}\ar[dr] && \ldots \\
             \ldots \ar[ur]\ar[dr] && {\begin{matrix} 2 \\ 1 \end{matrix}}\ar[ur]\ar[dr] && { \begin{matrix} 3 \\ 2 \end{matrix}}\ar[ur]\ar[dr] && {\begin{matrix} 4 \\ 3 \end{matrix}}\ar[ur]\ar[dr] &&  {\begin{matrix} 3 \\ 2 \\ 1 \end{matrix}[1]}\ar[ur]\ar[dr] && {\begin{matrix} 4 \\ 3 \\2 \end{matrix}[1]}\ar[ur]\ar[dr] & \\
              &{\begin{matrix} 4 \\ 3 \end{matrix}[-1]}\ar[ur]\ar[dr] && {\begin{matrix} 3 \\ 2 \\ 1 \end{matrix}}\ar[ur]\ar[dr] && {\begin{matrix} 4 \\ 3 \\2 \end{matrix}}\ar[ur]\ar[dr] && {\begin{matrix} 2 \\ 1 \end{matrix}[1]}\ar[ur]\ar[dr] && { \begin{matrix} 3 \\ 2 \end{matrix}[1]}\ar[ur]\ar[dr]  && \ldots &&&&\\
             \ldots \ar[ur] && \begin{matrix} 4 \end{matrix}[-1]\ar[ur] && {\begin{matrix} 4 \\ 3 \\2 \\ 1 \end{matrix}}\ar[ur] && \begin{matrix} 1 \end{matrix}[1]\ar[ur] && \begin{matrix} 2 \end{matrix}[1]\ar[ur] && \begin{matrix} 3 \end{matrix}[1]\ar[ur]  & \\
   }}$$ Here we denoted 