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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?
You could copy-paste from my answer here. The proof in the Elephant is for a more general situation.
Okay, did that.
added pointer to:
Cynthia Lester, Covers in the Canonical Grothendieck Topology (arXiv:1909.03384)
Cynthia Lester, The canonical Grothendieck topology and a homotopical analog, 2019 (uoregon:1794/24924 pdf)
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