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It is well known that for $E$ a Grothendieck topos, (by appropriately making use of universes) $E$ carries the canonical Grothendieck topology generated by jointly surjective epimorphisms, say $J$, such that $Sh_J\left(E\right) \simeq E$. Is there an analogous statement for infinity topoi?

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You may have a look at Remark and Lemma in Lurie's book. –  Denis-Charles Cisinski Dec 13 '11 at 22:16
Great, just what I needed thanks! –  David Carchedi Dec 13 '11 at 22:34

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