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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 28th 2015
   • (edited May 28th 2015)
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   Author: Urs
   Format: MarkdownItexI see that (from long, long time ago) one section of the entry _[[graded vector space]]_ defines "pre-graded" to mean $\mathbb{Z}$-graded and "graded" to be $\mathbb{N}$-graded. I am not sure if that is a good terminology, mainly because it seems not to be common. I came here from the entry _[[dg-Lie algebra]]_, wondering what that entry might actually mean by a "pre-graded" Lie algebra. (I should have commented on this long ago, of course).

   I see that (from long, long time ago) one section of the entry graded vector space defines “pre-graded” to mean -graded and “graded” to be -graded.

   I am not sure if that is a good terminology, mainly because it seems not to be common. I came here from the entry dg-Lie algebra, wondering what that entry might actually mean by a “pre-graded” Lie algebra. (I should have commented on this long ago, of course).

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeMay 28th 2015
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   Author: Mike Shulman
   Format: MarkdownItexWeird. I've never ever heard that terminology. Where does it come from?

   Weird. I’ve never ever heard that terminology. Where does it come from?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 28th 2015
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   Author: Urs
   Format: MarkdownItexTim will know more, I suppose. (?) But I'd suggest that even if it comes from somewhere, we should deprecate it. And at _[[dg-Lie algebra]]_ we should accordingly edit to make it clear that in general in fact dg-Lie algebras are $\mathbb{Z}$-graded.

   Tim will know more, I suppose. (?) But I’d suggest that even if it comes from somewhere, we should deprecate it. And at dg-Lie algebra we should accordingly edit to make it clear that in general in fact dg-Lie algebras are -graded.

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeMay 28th 2015
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   Author: Tim_Porter
   Format: MarkdownItexThose pages were initially my attempt to understand Daniel Tanré's lecture notes. I struck with his terminology at the time. I now find it awkward! $\mathbb{Z}$-graded is much clearer.

   Those pages were initially my attempt to understand Daniel Tanré’s lecture notes. I struck with his terminology at the time. I now find it awkward! -graded is much clearer.

5. • CommentRowNumber5.
   • CommentAuthorleo_schelstraete
   • CommentTimeSep 22nd 2023
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   Author: leo_schelstraete
   Format: MarkdownItexIs the formula $(f\otimes g) (v\otimes w) = (-1)^{|g||f|}(f(v) \otimes g(w))$ the intended one (last section on the tensor product)? For me the formula $(f\otimes g) (v\otimes w) = (-1)^{|g||v|}(f(v) \otimes g(w))$ is the standard one, and the associated category is not monoidal, but rather supermonoidal.

   Is the formula the intended one (last section on the tensor product)? For me the formula is the standard one, and the associated category is not monoidal, but rather supermonoidal.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 22nd 2023
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   Author: Urs
   Format: MarkdownItexThanks for the heads-up. This formula is from [revision 9](https://ncatlab.org/nlab/revision/diff/graded+vector+space/9). I am not sure what the intention of this category of "pre-gvs" really is.

   Thanks for the heads-up. This formula is from revision 9.

   I am not sure what the intention of this category of “pre-gvs” really is.