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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2011
    • (edited Nov 8th 2012)

    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

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2011

    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

    Π X(XH/X)Π(XH). \Pi_X(X \in \mathbf{H}/X) \simeq \Pi(X \in \mathbf{H}) \,.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2012

    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.

    • CommentRowNumber4.
    • CommentAuthorDavidCarchedi
    • CommentTimeJun 10th 2020

    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).

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 11th 2020

    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).

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