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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010

    I created fundamental ∞-groupoid of a locally ∞-connected (∞,1)-topos in an attempt to draw together a thread that so far existed only (as far as I could tell) in subsections of shape of an (∞,1)-topos and geometric homotopy groups in an (∞,1)-topos.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 28th 2010
    • (edited Oct 28th 2010)

    I worked a bit on the entry. You should check if you are still happy with it.

    Mainly I tried to structure the material a bit more. For instance I put the pieces together for the proof of the reflection GrpdΠLC(,1)Topos\infty Grpd \stackrel{\overset{\Pi}{\leftarrow}}{\hookrightarrow} LC(\infty,1)Topos.

    Also, I (finally) created fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos (in instead of of :-) and started replacing links to path infinity-groupoid (schreiber) with links to this entry.

    Also I added the observation that the internal and external definition of fundamental \infty-groupoids on an ELCtoposE \in LC\infty topos agree on every XEX \in E:

    Π E(X)Π(E/X). \Pi_E(X) \simeq \Pi(E/X) \,.

    Trivial, but important.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2010

    Looks good!