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    • CommentRowNumber1.
    • CommentAuthorLee Wang
    • CommentTimeAug 4th 2020
    I believe there is some consensus what a 2-Grothendieck topos should be, characterizing 2-stacks on 2-sites. What are the corresponding 2-geometric morphisms? Preserving finite weighted limits, all weighted colimits perhaps?
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeAug 5th 2020

    Yes. Given the adjoint 2-functor theorem, the latter should be equivalent to being a left adjoint.