Recall that a map of schemes, algebraic spaces, stacks, etc is called *submersive* if the associated map on underlying topological spaces is a quotient map. Recall moreover that a map is called universally submersive if it is submersive and all of its base changes are submersive.

Recall that a map $f:b\to b^\prime$ is called an $E$-descent morphism relative to a Cartesian fibration $E\to B$ if the natural map $E_{b^\prime}\to E_{S_f}$ is fully faithful, where $E_{S_f}$ is the value of $E$ on the $b^\prime$-sieve $S_f$ generated by $f$. A map $b\to b^\prime$ is a universal E-descent morphism if all of its base-changes are E-descent morphisms.

In SGA4 VIII 9.3, there is a theorem demonstrating that universally submersive maps of schemes are universal descent morphisms for the Cartesian fibration on the category of schemes sending a scheme $S$ to the category of étale sheaves of sets on $S$ with transition morphisms given by the pullback functors.

Two questions:

1.) Are universally submersive maps of schemes also universal descent maps for the $(2,1)$-stack sending a scheme $S$ to the $(2,1)$-category of étale sheaves of groupoids on $S$? How about the $(n+1,1)$-stack of sheaves of n-groupoids?

2.) Can this be extended to the case where we replace the category of schemes with the $(2,1)$-category of Artin stacks (or Deligne-Mumford stacks)? Do we have to add more adjectives to 'universally submersive' to make it hold in this more general context (for example, representable universally submersive, locally separated universally submersive, etc)?

The original proof in SGA uses a very cute trick, but it doesn't seem to apply once you throw stacks in the mix (it uses the fact that any map admitting a section is a mono, and this fails very badly for stacks).

Edit: I added a bounty. What's left to understand is the case of a universal submersion of ordinary schemes (whether these are universal descent morphisms for the fibration of étale n-sheaves)

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