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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2011

    In reaction to the public demand exhibited by Guillaume Brunerie's comments I have created an entry

    base (infinity,1)-topos.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2011

    I would expect that infinity-topoi over base or not form a (,2)(\infty,2)-category. Are you saying that up-to-set theoretic problems the (,1)(\infty,1)-decategorification of it is in fact a (,1)(\infty,1)-topos ?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2011

    I would expect that infinity-topoi over base or not form a (∞,2)-category.

    Sure, if you regard (,1)Topos(\infty,1)Topos as an (,2)(\infty,2)-category, then all its slices are, too.

    Are you saying that up-to-set theoretic problems the (∞,1)-decategorification of it is in fact a (∞,1)-topos ?

    No, why do you say that?

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2011

    Oh I see: over-(infinity%2C1)-topos says it clearly.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2011

    Oh I see: over-(infinity%2C1)-topos says it clearly.

    I am not sure what you mean. Working over a base topos means slicing the 2-category of all toposes over a fixed base topos, not slicing a fixed topos over one of its objects.

    On the other hand every such over-topos has the original topos as a base topos. Is that what you are thinking of?