The setting for this question is the (2,1) category Topoi.

- 0-cells in Topoi are Grothendieck topoi.
- 1-cells are geometric morphisms and have the direction of the right adjoint.
- 2-cells are invertible natural transformation (between the left adjoints).

Johnstone (and Lurie) proves that this 2-category has pseudo colimits that can be computed in Cat. To be precise, given a diagram in Topoi its colimit is the limit of the corresponding diagram in Cat associated to the inverse images.

Q.Does the representable functor $\mathsf{pt}:= \text{Topoi(Set, )} $ preserve directed colimits?

After some naive optimism, I have the feeling that the answer is *no*, but I suspect that it might be known.

- A candidate counterexample would be a topos $\mathcal{E}$ whose subtopoi lattice is not infinitary distributive, in fact a point is an atom in this coHeyting algebra.
- Another idea is to build a topos with with some points as a directed colimit of topoi without points, but I am not sure that this is possible at all.
- If a counterexample exist, I expect that it's possible to exhibit a
*localic*counterexample.