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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2009
   • PermaLink
   Author: Urs
   Format: Markdownadded recent AlgTop mailing list contribution on fibrant replacement of cubical sets to [[cubical set]]

   added recent AlgTop mailing list contribution on fibrant replacement of cubical sets to cubical set

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 27th 2013
   • (edited Sep 27th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded a pointer to * [[Thierry Coquand]], Simon Huber, _A model of type theory in cubical sets_ ([pdf](http://www.cse.chalmers.se/~coquand/mod1.pdf))

   Added a pointer to

   • Thierry Coquand, Simon Huber, A model of type theory in cubical sets (pdf)
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 20th 2014
   • (edited Oct 20th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded the remark (at the end of [this](http://ncatlab.org/nlab/show/model+structure+on+cubical+sets#HomotopyTheory) paragraph) that Jardine's result implies not just that the homotopy category of cubical set is equivalent to that of simplicial sets, but that the $\infty$-categories are in fact equivalent. Same remark at the relevant [point](http://ncatlab.org/nlab/show/cubical+set#ModelCategoryStructureAndHomotopyTheory) in the entry on cubical sets itself. (Thanks to Mike for reminiding me that Jardine indeed shows that the unit and counit of the adjunction are weak equivalences.)

   Added the remark (at the end of this paragraph) that Jardine’s result implies not just that the homotopy category of cubical set is equivalent to that of simplicial sets, but that the $\infty$-categories are in fact equivalent.

   Same remark at the relevant point in the entry on cubical sets itself.

   (Thanks to Mike for reminiding me that Jardine indeed shows that the unit and counit of the adjunction are weak equivalences.)