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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 $\mathbb{Z}$-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).

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 $\mathbb{Z}$-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! $\mathbb{Z}$-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 $(f\otimes g) (v\otimes w) = (-1)^{|g||f|}(f(v) \otimes g(w))$ 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.

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.