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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2010
   • (edited Jun 17th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am trying to remove the erroneous shifts in degree by $\pm 1 $ that inevitably I have been making at [[simplicial skeleton]] and maybe at [[truncated]]. So a Kan complex is the nerve of an $n$-groupoid iff it is $(n+1)$-coskeletal, I hope ;-) At [[truncated]] in the examples-section i want to be claiming that the truncation adjunction in a general (oo,1)-topos is in the case of $\infty$Grpd the $(tr_{n+1} \dashv cosk_{n+1})$-adjunction on Kan complexes. But I should be saying this better.

   I am trying to remove the erroneous shifts in degree by $\pm 1$ that inevitably I have been making at simplicial skeleton and maybe at truncated.

   So a Kan complex is the nerve of an $n$-groupoid iff it is $(n+1)$-coskeletal, I hope ;-)

   At truncated in the examples-section i want to be claiming that the truncation adjunction in a general (oo,1)-topos is in the case of $\infty$Grpd the $(tr_{n+1} \dashv cosk_{n+1})$-adjunction on Kan complexes. But I should be saying this better.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2010
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   Author: Urs
   Format: MarkdownItexI typed out now what I think is a complete proof, see <a href="http://ncatlab.org/nlab/show/n-truncated+object+of+an+(infinity%2C1)-category#InInfGrpd">Truncation in ooGrpd</a>.

   I typed out now what I think is a complete proof, see Truncation in ooGrpd.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2010
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   Author: Urs
   Format: MarkdownItexadded some propositions and proofs on properties of truncation to <a href="http://ncatlab.org/nlab/show/n-truncated+object+of+an+(infinity%2C1)-category#GeneralPropsTruncation">Truncation - Properties - General</a>

   added some propositions and proofs on properties of truncation to Truncation - Properties - General

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 18th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded more details on the proof of the recursive definition of k-truncated morphisms <a href="http://ncatlab.org/nlab/show/n-truncated+object+of+an+(infinity%2C1)-category#RecursiveDefinition">here</a>.

   added more details on the proof of the recursive definition of k-truncated morphisms here.