John Baez's constraints for subsets can also be given by the diagram,
\$\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?