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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 26th 2011

have created an entry separated (2,1)-presheaf

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 26th 2011

and just for completeness: separated (infinity,1)-presheaf

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJan 26th 2011

Shouldn’t there be a notion of k-separated (n,1)-presheaf?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 26th 2011

Yes, certainly. If all morphisms $X(U) \to Desc(U,X)$ are $(k-2)$-truncated morphisms, then $X$ is $k$-separated. As you know. But I should not spend more time on this right now.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJan 26th 2011

Okay, if I have the time to make the remark here, I can also make it in the $n$Lab entry, I guess. So I added a sentence and a half to separated (infinity,1)-presheaf