Categorizer Function

The categorizer function $\mathsf{Cat}_F \colon A \to (0,1]$ is the unique function with $\mathsf{Cat}_F(a) = 1$ if $a^-$ $= \emptyset$ and $\mathsf{Cat}_F(a) = \frac{1}{1 + \sum_{b \in a^-} \mathsf{Cat}_F(b)}$ otherwise.