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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1You may have a look at Remark 6.3.5.17 and Lemma 6.3.5.28 in Lurie's book. – D.-C. Cisinski Dec 13 '11 at 22:16