>Puzzle 122. Let C be the free category on this graph:

>

>Let's use this as a database schema. Draw an example of a database built using this schema. Mathematically it's a functor F:Câ†’Set. But what does this mean in concrete terms? You can draw it as a table, like you would see in a spreadsheet.

Giving an instance to the above free-category \\(C\\), just produces something that looks like a 2 column table,

\\[

\begin{array}{c|c}

\text{People} & \mathrm{FriendOf} \\\\

\hline

Alice & Bob \\\\

Bob & Alice \\\\

\vdots & \vdots \\\\

Stan & Tyler \\\\

Tyler & Stan. \\\\

\vdots & \vdots

\end{array}

\\]

>

>Let's use this as a database schema. Draw an example of a database built using this schema. Mathematically it's a functor F:Câ†’Set. But what does this mean in concrete terms? You can draw it as a table, like you would see in a spreadsheet.

Giving an instance to the above free-category \\(C\\), just produces something that looks like a 2 column table,

\\[

\begin{array}{c|c}

\text{People} & \mathrm{FriendOf} \\\\

\hline

Alice & Bob \\\\

Bob & Alice \\\\

\vdots & \vdots \\\\

Stan & Tyler \\\\

Tyler & Stan. \\\\

\vdots & \vdots

\end{array}

\\]