(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
By categorification of the notion of geometric morphism, an -geometric morphism is a pair of adjoint (∞,1)-functors between (∞,1)-toposes where the leftadjoint is left-exact.
For and two (∞,1)-toposes, a -geometric morphism is
(called the direct image of the geometric morphism)
which has a left adjoint (∞,1)-functor ;
(called the inverse image of the geometric morphism)
such that is a left exact (∞,1)-functor.
The (non-full) sub-(∞,1)-category of (∞,1)Cat on (∞,1)-toposes and -geometric morphisms between them is (∞,1)Toposes.
section 6.3.1 in
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