I've got a wondering about how [stuff, structure, and properties](https://ncatlab.org/nlab/show/stuff,+structure,+property) fits into databases.

In the example of transforming databases from [Lecture 41](https://forum.azimuthproject.org/discussion/2230/lecture-41-chapter-3-composing-functors), the functor that ignores departmental data is full and faithful but not essentially surjective. So it "forgets at most properties". I can't figure out how to think of departmental data as a property but maybe I am trying to take the analogy too far?

In the example from this lecture, I think that \$$F: \mathcal D \to \mathcal C\$$ is full and essentially surjective so it forgets at most stuff. So maybe it makes sense to think of nationality as "stuff" (or information) that a person has.

Here is another example. Consider let \$$\mathcal E\$$ be the free graph on

![](http://slibkind.github.io/act/acquaintance.png)

And let \$$H: \mathcal{E} \to \mathcal{C}\$$ map the acquaintance morphism to the morphism \$$\textrm{FriendOf} \circ \textrm{FriendOf}\$$. \$$H\$$ is essentially surjective and faithful so it forgets at most structure.