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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 $\infty Grpd \stackrel{\overset{\Pi}{\leftarrow}}{\hookrightarrow} LC(\infty,1)Topos$.

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 $E \in LC\infty topos$ agree on every $X \in E$:

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

Trivial, but important.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeOct 28th 2010

Looks good!