\[ \textbf{Gr} \overset{G}{\rightarrow} \textbf{DDS} \overset{I}{\rightarrow} \textbf{Set} \]

\\( G.I : \textbf{Gr} \rightarrow \textbf{Set} \\)
\[
\begin{matrix}
\begin{array}{c | c c}
\text{Arrow} & \text{source} & \text{target} \\\\
\hline
1 & 4 & 1 \\\\
2 & 4 & 2 \\\\
3 & 5 & 3 \\\\
4 & 5 & 4 \\\\
5 & 5 & 5 \\\\
6 & 7 & 6 \\\\
7 & 6 & 7
\end{array}
&
\begin{array}{c}
\text{Vertex} \\\\
\hline
1 \\\\
2 \\\\
3 \\\\
4 \\\\
5 \\\\
6 \\\\
7
\end{array}
\end{matrix}
\]

\\( G.K : \textbf{Gr} \rightarrow \textbf{Drawings} \\)

![diagram](https://docs.google.com/drawings/d/e/2PACX-1vQlQFvbsNfcZ8yERWP3UZq2rawZEpAM1MeFvqPHNGCptosDnYjgOYklW3x-SuYPIrxMFk2Zl-s_e7Rv/pub?w=427&h=240)

There is a functor that maps the set-instance functor \\( GI : \textbf{Gr} \rightarrow \textbf{Set} \\) to a diagram-instance functor \\( GK : \textbf{Gr} \rightarrow \textbf{Drawing} \\)?