(My apologies if this is well-known: I feel that I'm missing something very obvious here.)

**Basic question:** Do filtered colimits exist in the effective topos?

The reason I feel I'm missing something very obvious is that Jaap van Oosten wrote en entire paper titled “Filtered colimits in the effective topos” (also pretty much reproduced as §3.8.2 of his book *Realizability: An Introduction to its Categorical Side*), whose title suggests that the answer should definitely be there if it's not obvious in the first place, but… I can't find anything about the *existence* of filtered colimits in the paper in question. There is an example (proposition 1.3 in the paper, 3.8.3 in the book) which shows that $\nabla\colon \mathrm{Set} \to \mathrm{Eff}$ doesn't preserve the colimit of the diagram of finite subsets $S \subseteq \mathbb{N}$ with inclusions between them, but that $\varinjlim(\nabla S)$ does not equal $\nabla\mathbb{N}$ doesn't tell me the former doesn't exist in $\mathrm{Eff}$. But van Oosten doesn't clarify the issue one way or another.

**Extended question:** Assuming the answer to the basic question is “no”, are there some interesting conditions that we can put either on the objects, or on the maps, or on the indexing system, or some combination thereof, that ensures the filtered colimit exists? For example, does the colimit of a system indexed by a totally ordered set whose transition maps are monomorphisms exist in $\mathrm{Eff}$?