[Frederick wrote:](https://forum.azimuthproject.org/discussion/comment/19393/#Comment_19393)

> In [comment 11](https://forum.azimuthproject.org/discussion/comment/19381/#Comment_19381) the candidates
for natural transformation, \$$\alpha\$$, are enumerated.
>
> > \$$F \Rightarrow G\$$, \$$G \Rightarrow H\$$ and \$$F\Rightarrow H\$$ by composition.
Likewise, \$$H\Rightarrow G\$$, \$$G \Rightarrow F\$$ and \$$H\Rightarrow F\$$.
By identity \$$F \Rightarrow F\$$, \$$G \Rightarrow G\$$ and \$$H \Rightarrow H\$$.
>
> But, we need to prune some of them away.
>
> In particular the natural transformation needs to have a morphism by which it may be realized in **3**.
Such a morphism is not present in the case of \$$H\Rightarrow G\$$, \$$G \Rightarrow F\$$ and \$$H\Rightarrow F\$$.

Just to corroborate, I get the same count.

I also count three identity morphisms, giving me a total of 6 - are we not supposed to be counting those?