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@@ -550,7 +550,7 @@ The order structure that we can define for this functor is that for sets $X$ and
\end{proof} \end{proof}
\subsection{Subdistribution Functor} \subsection{Subdistribution Functor}
The subdistribution functor $\sub\c\Set\to\Set$ is defined as $\sub X=\{\mu\c X\to[0,1]\mid \sum_{x\in X}\mu(x)\}$ on objects, and for $\sub f\c \sub X\to\sub Y$, we have The subdistribution functor $\sub\c\Set\to\Set$ is defined as $\sub X=\{\mu\c X\to[0,1]\mid \sum_{x\in X}\mu(x)\leq 1\}$ on objects, and for $\sub f\c \sub X\to\sub Y$, we have
\begin{gather*} \begin{gather*}
\sub f(\mu)=y\mapsto\sum_{x\in f^{\mone}(y)}\mu(x), \sub f(\mu)=y\mapsto\sum_{x\in f^{\mone}(y)}\mu(x),
\end{gather*} \end{gather*}