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\begin{struct}\label{pointed_set}
A pointed set $X$ is a onesorted structure equipped with
\begin{enumerate}
\item $\pick$
\end{enumerate}
such that
\begin{enumerate}
\item\label{pointed_refl} $X = X$.
\end{enumerate}
\end{struct}
\begin{proposition}\label{pointed_carrier}
Let $X$ be a pointed set.
Let $x \in X$.
Then $x \in \carrier[X]$.
\end{proposition}
\begin{proof}
Follows by assumption.
\end{proof}
\begin{proposition}\label{pointed_operation}
Let $X$ be a pointed set.
Then $\pick = \pick[X]$.
\end{proposition}
\begin{proof}
Follows by assumption.
\end{proof}
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