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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 5th 2011
   • (edited Nov 8th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave tried to brush-up the entry [[locally infinity-connected (infinity,1)-topos]]. Kicked out a bunch of material that we had meanwhile copied over to their dedicated entries and tried to organize the remaining material a bit better. Need to work on [[locally infinity-connected site]]

   have tried to brush-up the entry locally infinity-connected (infinity,1)-topos.

   Kicked out a bunch of material that we had meanwhile copied over to their dedicated entries and tried to organize the remaining material a bit better. Need to work on locally infinity-connected site

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2011
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   Author: Urs
   Format: MarkdownItexhave added at [[locally infinity-connected (infinity,1)-topos]] the observation that the potentially two notions of geometric fundamental $\infty$-groupoid of an object in such a beast agree $$ \Pi_X(X \in \mathbf{H}/X) \simeq \Pi(X \in \mathbf{H}) \,. $$

   have added at locally infinity-connected (infinity,1)-topos the observation that the potentially two notions of geometric fundamental $\infty$-groupoid of an object in such a beast agree

   $$\Pi_X(X \in \mathbf{H}/X) \simeq \Pi(X \in \mathbf{H}) \,.$$
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 8th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the remark (and simple proof) [here](http://ncatlab.org/nlab/show/locally+n-connected+%28n%2B1%2C1%29-topos#RelationToLocallyConnectedToposes) that the 1-topos underlying a (locally/globally/strongly) $\infty$-connected $\infty$-topos is itself a (locally/globally/strongly) connected topos.

   added the remark (and simple proof) here that the 1-topos underlying a (locally/globally/strongly) $\infty$-connected $\infty$-topos is itself a (locally/globally/strongly) connected topos.

4. • CommentRowNumber4.
   • CommentAuthorDavidCarchedi
   • CommentTimeJun 10th 2020
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   Author: DavidCarchedi
   Format: MarkdownItexI can't seem to find the thread for the page this has now been merged with (locally n-connected (n+1,1)-topos), but Example 3.4 is wrong (or at least its proof is): The subsite on contractible opens is not closed under finite limits, so it does not necessarily yield the same infinity-topos of sheaves unless you take hypersheaves (unless you have a proof of hypercompletion in this setting).

   I can’t seem to find the thread for the page this has now been merged with (locally n-connected (n+1,1)-topos), but Example 3.4 is wrong (or at least its proof is): The subsite on contractible opens is not closed under finite limits, so it does not necessarily yield the same infinity-topos of sheaves unless you take hypersheaves (unless you have a proof of hypercompletion in this setting).

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 11th 2020
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   Author: Urs
   Format: MarkdownItexHi David, thanks for the alert. Right, that is the kind of gap that you and Marc had been addressing [back then](https://mathoverflow.net/q/130999/381). I have been trying to fix this where I could, but missed it here and likely elsewhere. I have fixed it in the entry now in a cheap way by just demanding hypercompleteness ([here](https://ncatlab.org/nlab/show/locally+n-connected+%28n%2B1%2C1%29-topos#OverLocallynConnectedTopologicalSpaces)).

   Hi David,

   thanks for the alert. Right, that is the kind of gap that you and Marc had been addressing back then. I have been trying to fix this where I could, but missed it here and likely elsewhere. I have fixed it in the entry now in a cheap way by just demanding hypercompleteness (here).