Question on gluing schemes

Stream: maths

[Dhyan Aranha]

I'd like try my hand at building some simple schemes via gluing ( say for example the affine line with doubled origin ). While, browsing Gluing, I looks like I want to use

def AlgebraicGeometry.Scheme.IsLocallyDirected.glueData

but there I found the following sentence rather cryptic:

One usually does not want to use this directly, and instead use the generic colimit API.

I was wondering what is meant by this?

[Christian Merten]

The sentence means that you should build a diagram of schemes (i.e. a docs#CategoryTheory.Functor) show it has a colimit (docs#CategoryTheory.Limits.HasColimit) and then take its docs#CategoryTheory.Limits.colimit.
The IsLocallyDirected API will give existence of colimits in some special cases.

[Christian Merten]

In particular, pushouts along open immersions exist, so you should take the pushout of two morphisms (i.e. docs#CategoryTheory.Limits.pushout) instead of using docs#AlgebraicGeometry.Scheme.IsLocallyDirected.glueData.
You should view the latter as an auxiliary construction to prove that certain colimits exist.