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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 6th 2011
• (edited Jan 6th 2011)

have created infinity-connected site

• moved over from infinity-cohesive site the proof that the $\infty$-topos over a locally and globally $\infty$-connected site is locally and globally $\infty$-connected; (and had occasion to polish and streamline it a bit more)
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

Wait, I made a mistake. am fixing it…

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

Sorry, I had written the claim that open subsets of a locally contractibe topological space forms an example of the current definition of locally $\infty$-connected site. But that is trivially wrong (since we have non-connected open subsets and hence constant $\infty$-presheaves are not $\infty$-sheaves). Now, possibly that just means that the definition is currently too coarse.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

Okay, so just a reminder for myself, lest I forget it once again (even though I just said it elsewher): the definition of $\infty$-connected locally $\infty$-connected site is good, but. the case of just locally $\infty$-connected sites needs more thinking.