If and are Grothendieck n-toposes, an -geometric morphism consists of an adjoint pair , where is the direct image and is the inverse image, such that preserves finite limits (in the -categorical sense).
When this is, of course, the usual definition. When this reduces to a continuous map between locales.
In general, we expect that Grothendieck -toposes satisfy an -categorical version of the adjoint functor theorem, so that any functor that preserves finite limits and small colimits is the inverse image of some -geometric morphism.
We define transformations and modifications between -geometric morphisms to be transformations and modifications between their inverse image functors. We then have an -category of Grothendieck -toposes and -geometric morphisms.