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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 28th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI tried to brush-up the entry [[fundamental infinity-groupoid]] which had been in a rather sorry state. Some things I did: * stated the definition (!) $Sing X$ * removed Ronnie's remark that there is a problem with this definition due to lack of chosen fillers and instead added Thomas Nikolaus's theorem that when you choose fillers to get an algebraic Kan complex $\Pi X$ there is (still) a direct proof of the homotopy hypothesis * made the statement that $Sing X$ is equivalently computed by the abstract $\infty$-topos-theoretic definition of fundamental $\infty$-groupoid a formal proposition.

   I tried to brush-up the entry fundamental infinity-groupoid which had been in a rather sorry state. Some things I did:

   • stated the definition (!) $Sing X$

   • removed Ronnie’s remark that there is a problem with this definition due to lack of chosen fillers and instead added Thomas Nikolaus’s theorem that when you choose fillers to get an algebraic Kan complex $\Pi X$ there is (still) a direct proof of the homotopy hypothesis

   • made the statement that $Sing X$ is equivalently computed by the abstract $\infty$-topos-theoretic definition of fundamental $\infty$-groupoid a formal proposition.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 28th 2010
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThat looks good. I added a comment before the definition to the effect that we're choosing Kan complexes as a notion of $\infty$-groupoid in order to make that definition.

   That looks good. I added a comment before the definition to the effect that we’re choosing Kan complexes as a notion of $\infty$-groupoid in order to make that definition.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexpolished up these two bibitems: * [[Keith A. Hardie]], [[Klaus H. Kamps]], [[Rudger Kieboom]], *A homotopy 2-groupoid of a Hausdorff space*. Papers in honour of Bernhard Banaschewski (Cape Town, 1996). Appl. Categ. Structures **8** (2000) 209-234 &lbrack;[doi:10.1023/A:1008758412196](https://doi.org/10.1023/A:1008758412196)&rbrack; * [[Keith A. Hardie]], [[Klaus H. Kamps]], [[Rudger Kieboom]], *A Homotopy Bigroupoid of a Topological Space*, Applied Categorical Structures **9** (2001) 311-327 &lbrack;[doi:10.1023/A:1011270417127](https://doi.org/10.1023/A:1011270417127)&rbrack; Will give them an entry *[[fundamental 2-groupoid]]* now (which has been missing all along, even as a redirect) <a href="https://ncatlab.org/nlab/revision/diff/fundamental+infinity-groupoid/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/fundamental+infinity-groupoid/26">v26</a>, <a href="https://ncatlab.org/nlab/show/fundamental+infinity-groupoid">current</a>

   polished up these two bibitems:

   • Keith A. Hardie, Klaus H. Kamps, Rudger Kieboom, A homotopy 2-groupoid of a Hausdorff space. Papers in honour of Bernhard Banaschewski (Cape Town, 1996). Appl. Categ. Structures 8 (2000) 209-234 [doi:10.1023/A:1008758412196]

   • Keith A. Hardie, Klaus H. Kamps, Rudger Kieboom, A Homotopy Bigroupoid of a Topological Space, Applied Categorical Structures 9 (2001) 311-327 [doi:10.1023/A:1011270417127]

   Will give them an entry fundamental 2-groupoid now (which has been missing all along, even as a redirect)

   diff, v26, current