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Descent of Higher categorical structures along geometric morphisms

What I want to known is whether one also have descent for Higher categorical structures in $\mathcal{E}$ ? … Or, even more optimistically do Grothendieck toposes in $\mathcal{E}$ satisfies a $2$-categorical version of descent (i.e. does open or proper surjections are effective descent morphism in the $(2,1)$- …
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