Anindya wrote:

> K, let's take \\(\mathcal{C}\\) to be the people/friend-of schema from [Lecture 42](https://forum.azimuthproject.org/discussion/2236/lecture-42-chapter-3-transforming-databases).

>

> And \\(\mathcal{D}\\) is the same category but without the friend-of arrow. There's only one choice for \\(G : \mathcal{D} \rightarrow \mathcal{C}\\), which is the obvious inclusion functor.

Yes, that's the example I had in mind! \\(\mathrm{Lan}_G\\) generates an infinite list of friends for any person, so if start with a database \\(H\\) with just one person, then form \\(\mathrm{Lan}_G(H)\\), then form \\(\mathrm{Lan}_G(H) \circ G\\), we've got an enormous database with that person and an infinite list of others.

> I'm guessing that the issue here is that the inclusion functor \\(G\\) is not full.

That sounds about right. It would be fun to work out necessary and sufficient conditions.

> K, let's take \\(\mathcal{C}\\) to be the people/friend-of schema from [Lecture 42](https://forum.azimuthproject.org/discussion/2236/lecture-42-chapter-3-transforming-databases).

>

> And \\(\mathcal{D}\\) is the same category but without the friend-of arrow. There's only one choice for \\(G : \mathcal{D} \rightarrow \mathcal{C}\\), which is the obvious inclusion functor.

Yes, that's the example I had in mind! \\(\mathrm{Lan}_G\\) generates an infinite list of friends for any person, so if start with a database \\(H\\) with just one person, then form \\(\mathrm{Lan}_G(H)\\), then form \\(\mathrm{Lan}_G(H) \circ G\\), we've got an enormous database with that person and an infinite list of others.

> I'm guessing that the issue here is that the inclusion functor \\(G\\) is not full.

That sounds about right. It would be fun to work out necessary and sufficient conditions.