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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 27th 2013

somebody asked me for the proof of the claim at canonical topology that for a Grothendieck topos $\mathbf{H}$ we have $\mathbf{H} \simeq Sh_{can}(\mathbf{H})$.

I have added to the entry pointers to the proof in Johnstone’s book, and to related discussion for $\infty$-toposes. Myself I don’t have more time right now, but maybe somebody feels inspired to write out some details in the nLab entry itself?

• CommentRowNumber2.
• CommentAuthorZhen Lin
• CommentTimeNov 27th 2013

You could copy-paste from my answer here. The proof in the Elephant is for a more general situation.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 27th 2013

Okay, did that.