Jonathan wrote:

> I was always quite confused by natural transformations, but it seems they're just a selection of morphisms in the target category? How interesting!

Yes!

Well, a **transformation** between functors \$$F, G : \mathcal{C} \to \mathcal{D}\$$ is just an arbitrary selection of a morphism \$$\alpha_x : F(x) \to G(x) \$$ in the target category for each object \$$x\$$ in the source category. That's enough to create the vertical 'struts' in this picture:

But it's **natural** when the squares with these struts as their vertical sides _commute_. And that's the cool part.

Your answer to Puzzle 126 is very nice, and the nugget of insight lurks here:

> Practically speaking, the inclusion map allows us to extend a database in a consistent way.

The commuting of the squares, which makes our transformation 'natural', is a kind of _consistency condition!_

> It is notable that the database instance \$$H\$$ replaces Stan with Bob as Tyler's friend, which ensures that all induced squares commute.