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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2021

    added cross-links of this ancient entry with higher topos theory and with 2-topos etc.

    Notice that there is an old unresolved discussion box here.

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 18th 2022
    • (edited Sep 18th 2022)

    i am removing the following old query box from the entry:

    +– {: .query} When you say ’a locale is not identical to its topos of sheaves’, you mean that the following square cannot be filled in with an equivalence in 2Cat2 Cat?

    (0,1)Top toposofsheaves (1,1)Top (0,1)Cat 1Cat \array { (0,1) Top & \overset{topos\:of\:sheaves}\longrightarrow & (1,1) Top \\ \downarrow & & \downarrow \\ (0,1) Cat & \longrightarrow & 1 Cat }

    —Toby =–

    But the answer to the question is: “Yes”; and maybe it’s really worth making this explicit: So I have kept the diagram in the entry, now re-rendered via tikzcd.

    diff, v6, current