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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeJan 14th 2015
   • (edited Jan 14th 2015)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAt [[bounded chain complex ]] should the indexation be for $n\in \mathbb{Z}$ rather than $n\in \mathbb{N}$? This makes no difference for bounded above, but does for bounded below. In fact at [[chain complex]] only complexes graded by the natural numbers are initially considered, yet in many places later on one needs them being $\mathbb{Z}$-graded otherwise the suspension / delooping set up gets very messy. I suggest all should be $\mathbb{Z}$-graded with a note added that $\mathbb{N}$-graded ones form a category equivalent to the full subcategory of $Ch(\mathbf{A})$ given by the non-negatively graded ones.

   At bounded chain complex should the indexation be for $n\in \mathbb{Z}$ rather than $n\in \mathbb{N}$? This makes no difference for bounded above, but does for bounded below.

   In fact at chain complex only complexes graded by the natural numbers are initially considered, yet in many places later on one needs them being $\mathbb{Z}$-graded otherwise the suspension / delooping set up gets very messy. I suggest all should be $\mathbb{Z}$-graded with a note added that $\mathbb{N}$-graded ones form a category equivalent to the full subcategory of $Ch(\mathbf{A})$ given by the non-negatively graded ones.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJan 15th 2015
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   Author: Mike Shulman
   Format: MarkdownItex> At [[bounded chain complex ]] should the indexation be for $n\in \mathbb{Z}$ rather than $n\in \mathbb{N}$? Yes, that seems right. > In fact at [[chain complex]] only complexes graded by the natural numbers are initially considered, yet in many places later on one needs them being $\mathbb{Z}$-graded It looks to me like the actual "Definition" section takes them to be $\mathbb{Z}$-graded, although the previous "Idea" section had mentioned onl the $\mathbb{N}$-graded ones (presumably so as to be able to refer to Dold-Kan).

   At bounded chain complex should the indexation be for $n\in \mathbb{Z}$ rather than $n\in \mathbb{N}$?

   Yes, that seems right.

   In fact at chain complex only complexes graded by the natural numbers are initially considered, yet in many places later on one needs them being $\mathbb{Z}$-graded

   It looks to me like the actual “Definition” section takes them to be $\mathbb{Z}$-graded, although the previous “Idea” section had mentioned onl the $\mathbb{N}$-graded ones (presumably so as to be able to refer to Dold-Kan).

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeJan 15th 2015
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   Author: Tim_Porter
   Format: MarkdownItexI have adjusted the wording a bit to straighten this out.

   I have adjusted the wording a bit to straighten this out.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJan 15th 2015
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks!

   Thanks!