Coproduct of Telescopes

The coproduct of telescopes is given by the intersection of their shared fields. This is a bit confusing, but makes sense when we consider the Morphisms of Telescopes to be Weakenings: the inclusions $\iota_{0}:\Gamma\to\Gamma+\Delta$, $\iota_{1}:\Delta\to\Gamma+\Delta$ must remove fields from $\Gamma$ and $\Delta$, resp, and the universal property ensures that we only remove the fields we need.