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Exercise 64 - Chapter 3

edited June 2018 in Exercises

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.

Previous Next

\( I : \textbf{DDS} \rightarrow \textbf{Set} \)

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

Comments

  • 1.
    edited May 2018

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

    diagram

    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} \\)?
  • 2.

    We pulled back I along G.

    diagram

    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)
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