> \\[
\begin{matrix}
T & \overset{i} \hookrightarrow & S\\\\
u\downarrow & & \downarrow \chi \\\\
\lbrace \texttt{true} \rbrace & \overset{\ulcorner \texttt{true} \urcorner}\hookrightarrow & \lbrace \texttt{true}, \texttt{false} \rbrace
\end{matrix} \\]
with the constraint,
\\[
(\chi \circ i)(t)= \left (\ulcorner \texttt{true} \urcorner \circ u \right )(t).
\\]
>
> **Puzzle KEP:** Viewing this diagram as a category, \\(\mathcal{C}\\), produce an instance \\(F : \mathcal{C} \to \mathbf{Set}\\). Do instances of the set \\(F(T)\\) always correspond to a subset of an instance of the set \\(F(S)\\)? Why or why not?

I'm not sure what you're getting at.

Can you say the answer Keith?