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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 12th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[Sullivan construction]] (I got annoyed that the entry didn't exist, but also don't feel like doing it justice right now)

   stub for Sullivan construction (I got annoyed that the entry didn’t exist, but also don’t feel like doing it justice right now)

2. • CommentRowNumber2.
   • CommentAuthorEric
   • CommentTimeMay 12th 2010
   • PermaLink
   Author: Eric
   Format: MarkdownItexIs Sullivan construction related to the fact that a category of spaces is opposite a category of algebras? So starting with a particular kind of algebra, you get a particular kind of space?

   Is Sullivan construction related to the fact that a category of spaces is opposite a category of algebras? So starting with a particular kind of algebra, you get a particular kind of space?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 12th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, sure it's related. Only that here instead of just "algebras of functions" you take "dg-algebras of differential forms."

   Yes, sure it’s related. Only that here instead of just “algebras of functions” you take “dg-algebras of differential forms.”

4. • CommentRowNumber4.
   • CommentAuthorEric
   • CommentTimeMay 12th 2010
   • PermaLink
   Author: Eric
   Format: MarkdownItexOne day I hope I will know enough math kung fu to be able to work out the category of spaces opposite the category of noncommutative dg-algebras.

   One day I hope I will know enough math kung fu to be able to work out the category of spaces opposite the category of noncommutative dg-algebras.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 12th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItex> the category of spaces opposite the category of noncommutative dg-algebras. Well, this will be something like the category of oo-groupoids whose spaces of k-morphisms may be non-commutative spaces. At least that's true for cosimplicial noncommutative algebras. And under forming normalized cochain complexes these turn into noncommutative dg-algebras. Now I am not sure if we have a non-commutative Dold-Kan correspondence that asserts that this passage is an equivalence. So i can't quite decide off the top of my head if every NC dg-algebra will come, up to equivalence, from a cosimplcial NC algebra (but I guess it does??).

   the category of spaces opposite the category of noncommutative dg-algebras.

   Well, this will be something like the category of oo-groupoids whose spaces of k-morphisms may be non-commutative spaces.

   At least that’s true for cosimplicial noncommutative algebras. And under forming normalized cochain complexes these turn into noncommutative dg-algebras.

   Now I am not sure if we have a non-commutative Dold-Kan correspondence that asserts that this passage is an equivalence. So i can’t quite decide off the top of my head if every NC dg-algebra will come, up to equivalence, from a cosimplcial NC algebra (but I guess it does??).