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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2011
   • (edited Jan 6th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave 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)

   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)
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexWait, I made a mistake. am fixing it...

   Wait, I made a mistake. am fixing it…

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexSorry, 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, 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.

   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.