[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?

> 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?