For **puzzle 128** I get three natural transformations:

1. \\(\\{\textrm{Bob} \mapsto \textrm{Bob}, \textrm{Alice} \mapsto \textrm{Alice}, \textrm{Tyler} \mapsto \textrm{Tyler}\\}\\)
2. \\(\\{\textrm{Bob} \mapsto \textrm{Bob}, \textrm{Alice} \mapsto \textrm{Alice}, \textrm{Tyler} \mapsto \textrm{Alice}\\}\\)
3. \\(\\{\textrm{Bob} \mapsto \textrm{Alice}, \textrm{Alice} \mapsto \textrm{Bob}, \textrm{Tyler} \mapsto \textrm{Bob}\\}\\)

Here is the diagram for the third mapping:

![](https://doneata.bitbucket.io/applied-category-theory/nat-trans-friend-of-small.png)

Note: in the above picture, the arrows are not morphisms but they depict element mappings by either the natural transformation \\(\alpha\\) (horizontal arrows) or the \\(H(\textrm{FriendOf})\\) function (vertical arrows).