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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownI keep working on the entry now titled [[homotopy groups in an (infinity,1)-topos]] (used to be "homotopy groups of an oo-stack"). The following subsections I added * <a href="http://ncatlab.org/nlab/show/homotopy+groups+in+an+(infinity%2C1)-topos#PiConstruction">The geometric fundamental oo-groupoid</a> * <a href="http://ncatlab.org/nlab/show/homotopy+groups+in+an+(infinity%2C1)-topos#GeomPiOfTermObj">Geometric Pi_oo of the terminal object in a locally connected oo-topos</a> * <a href="http://ncatlab.org/nlab/show/homotopy+groups+in+an+(infinity%2C1)-topos#Pi0InLocConTop">Geometric Pi_0 of a genral object in a locally connected topos</a> * <a href="http://ncatlab.org/nlab/show/homotopy+groups+in+an+(infinity%2C1)-topos#GeneralExamples">Examples</a> (meaning: general examples, neither purely categorical nor geometrical, currently a discussion of simple examples that distinguish the two notions) This all needs more work. But I'll stop for a moment and instead start now an entry on locally n-connected (oo,1)-toposes, which I need for further discussion here.

   I keep working on the entry now titled homotopy groups in an (infinity,1)-topos (used to be "homotopy groups of an oo-stack").

   The following subsections I added

   • The geometric fundamental oo-groupoid

   • Geometric Pi_oo of the terminal object in a locally connected oo-topos

   • Geometric Pi_0 of a genral object in a locally connected topos

   • Examples (meaning: general examples, neither purely categorical nor geometrical, currently a discussion of simple examples that distinguish the two notions)

   This all needs more work. But I'll stop for a moment and instead start now an entry on locally n-connected (oo,1)-toposes, which I need for further discussion here.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 24th 2010
   • PermaLink
   Author: Urs
   Format: Markdownadded a brief section on n-connected and n-truncated objects to [[homotopy groups in an (infinity,1)-topos]]

   added a brief section on n-connected and n-truncated objects to homotopy groups in an (infinity,1)-topos

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2010
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   Author: Urs
   Format: MarkdownItexThe entry became too long for my taste, now that I want to work on the first part, so I split it into two sub-entries 1. [[categorical homotopy groups in an (infinity,1)-topos]] 1. [[geometric homotopy groups in an (infinity,1)-topos]]

   The entry became too long for my taste, now that I want to work on the first part, so I split it into two sub-entries

   1. categorical homotopy groups in an (infinity,1)-topos

   2. geometric homotopy groups in an (infinity,1)-topos