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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 15th 2012
   • (edited Jul 16th 2012)
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   Author: Dmitri Pavlov
   Format: MarkdownThe article [[spectrum]] claims that "There is a stabilized Dold-Kan correspondence that identifies these with special objects in Sp(Top)." The formula that follows this statement seems to imply that the stabilized Dold-Kan correspondence works with chain complexes that are unbounded in both directions. What is the reference for this type of Dold-Kan correspondence?

   The article spectrum claims that "There is a stabilized Dold-Kan correspondence that identifies these with special objects in Sp(Top)." The formula that follows this statement seems to imply that the stabilized Dold-Kan correspondence works with chain complexes that are unbounded in both directions. What is the reference for this type of Dold-Kan correspondence?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJul 16th 2012
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   Author: Mike Shulman
   Format: MarkdownItexI'm going to hope someone else has a good answer to your question, but just FYI, on the nForum you can type `[[spectrum]]` and it will automatically produce a link to the appropriate nLab page [[spectrum]], as long as you select the radio button "Markdown+Itex" below the input box.

   I’m going to hope someone else has a good answer to your question, but just FYI, on the nForum you can type [[spectrum]] and it will automatically produce a link to the appropriate nLab page spectrum, as long as you select the radio button “Markdown+Itex” below the input box.

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 16th 2012
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   Author: Dmitri Pavlov
   Format: Markdown@Mike: Thanks, I fixed it.

   @Mike: Thanks, I fixed it.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 16th 2012
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   Author: Urs
   Format: MarkdownItexThe entry discussing this is at _[[module spectrum]]_ in the section _[Stable Dold-Kan correspondence](http://ncatlab.org/nlab/show/module+spectrum#StableDoldKanCorrespondence)_. I am adding the missing pointers to that entry now to _[[spectrum]]_ and to _[[Dold-Kan correspondence]]_.

   The entry discussing this is at module spectrum in the section Stable Dold-Kan correspondence.

   I am adding the missing pointers to that entry now to spectrum and to Dold-Kan correspondence.

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 16th 2012
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   Author: Dmitri Pavlov
   Format: Markdown@Urs: Thanks a lot!

   @Urs: Thanks a lot!

6. • CommentRowNumber6.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 22nd 2012
   • (edited Jul 22nd 2012)
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   Author: Dmitri Pavlov
   Format: TextBy the way, what is currently written at [[module spectrum]] is only a half of what I would name the stabilized Dold-Kan correspondence. More precisely, the ordinary Dold-Kan correspondence says that the following three categories are equivalent: 1) Connective modules over HZ 2) Connective chain complexes of abelian groups 3) Simplicial abelian groups Similarly, the stabilized Dold-Kan correspondence says that the following three categories are equivalent: 1) Modules over HZ 2) Chain complexes of abelian groups 3) Stably-simplicial abelian groups 3) was defined in Kan's paper Semisimplicial spectra, who calls them abelian group spectra, see Definition 5.1. Proposition 5.8 proves an equivalence between 2) and 3).

   By the way, what is currently written at module spectrum is only a half of what I would name the stabilized Dold-Kan correspondence.
   
   More precisely, the ordinary Dold-Kan correspondence says that the following three categories are equivalent:
   1) Connective modules over HZ
   2) Connective chain complexes of abelian groups
   3) Simplicial abelian groups
   
   Similarly, the stabilized Dold-Kan correspondence says that the following three categories are equivalent:
   1) Modules over HZ
   2) Chain complexes of abelian groups
   3) Stably-simplicial abelian groups
   
   3) was defined in Kan's paper Semisimplicial spectra, who calls them abelian group spectra, see Definition 5.1.
   Proposition 5.8 proves an equivalence between 2) and 3).
7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2012
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   Author: Urs
   Format: MarkdownItexSounds very good. Do you feel like adding comments to this extent to one of the relevant entries?

   Sounds very good. Do you feel like adding comments to this extent to one of the relevant entries?

8. • CommentRowNumber8.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 19th 2012
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   Author: Dmitri Pavlov
   Format: MarkdownI added a new section on the stable Dold-Kan correspondence to [[Dold-Kan correspondence]]. I am now not at all sure if we should also refer to the theorem that establishes an equivalence of ∞-categories between HZ-modules and chain complexes as the Dold-Kan correspondence. This statement doesn't seem to be related in any way to the original results of Dold and Kan. Any suggestions on how to resolve this terminological problem?

   I added a new section on the stable Dold-Kan correspondence to Dold-Kan correspondence.

   I am now not at all sure if we should also refer to the theorem that establishes an equivalence of ∞-categories between HZ-modules and chain complexes as the Dold-Kan correspondence. This statement doesn't seem to be related in any way to the original results of Dold and Kan. Any suggestions on how to resolve this terminological problem?