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# Exercise 64 - Chapter 3

edited June 2018

Consider the functor $$G : \textbf{Gr} \rightarrow \textbf{DDS}$$ given by sending ‘source’ to ‘next’ and sending ‘target’ to the identity on ‘State’. Migrate the same data using $$G$$. Write down the tables and draw the corresponding graph.

$$I : \textbf{DDS} \rightarrow \textbf{Set}$$

$$\begin{array}{c | c} State & next \\ \hline 1 & 4 \\ 2 & 4 \\ 3 & 5 \\ 4 & 5 \\ 5 & 5 \\ 6 & 7 \\ 7 & 6 \end{array}$$

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edited May 2018

$$\textbf{Gr} \overset{G}{\rightarrow} \textbf{DDS} \overset{I}{\rightarrow} \textbf{Set}$$ $$G.I : \textbf{Gr} \rightarrow \textbf{Set}$$ $$\begin{matrix} \begin{array}{c | c c} \text{Arrow} & \text{source} & \text{target} \\ \hline 1 & 4 & 1 \\ 2 & 4 & 2 \\ 3 & 5 & 3 \\ 4 & 5 & 4 \\ 5 & 5 & 5 \\ 6 & 7 & 6 \\ 7 & 6 & 7 \end{array} & \begin{array}{c} \text{Vertex} \\ \hline 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \end{array} \end{matrix}$$ $$G.K : \textbf{Gr} \rightarrow \textbf{Drawings}$$

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

Comment Source:$\textbf{Gr} \overset{G}{\rightarrow} \textbf{DDS} \overset{I}{\rightarrow} \textbf{Set}$ \$$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} \$$? 
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We pulled back I along G.

Comment Source:We _pulled back_ I along G. ![diagram](https://docs.google.com/drawings/d/e/2PACX-1vQkfkH8NY7V6UFehWDb1sccXm33BaS6ENOCHeGzb_6oZdicWffNe-vn5Yx5kUw133XkYEcRPQ33iVoI/pub?w=191&h=181)