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).