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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 13th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[perfect complex]]

   stub for perfect complex

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeDec 13th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownItex> it is bounded from above and below; There are 3 concepts: bounded above, bounded below and just bounded which means that it is simultaneously bounded both above and below. Of course terminology left/right is also in use.

   it is bounded from above and below;

   There are 3 concepts: bounded above, bounded below and just bounded which means that it is simultaneously bounded both above and below. Of course terminology left/right is also in use.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 13th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I linked to [[bounded chain complex]]

   Okay, I linked to bounded chain complex

4. • CommentRowNumber4.
   • CommentAuthoradeelkh
   • CommentTimeJul 2nd 2013
   • (edited Jul 2nd 2013)
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexIs the definition on this page standard? I've only seen the definition for modules over a [ring](http://stacks.math.columbia.edu/tag/0656) or [ringed space](http://stacks.math.columbia.edu/tag/08CL) and they don't seem to be in exact agreement with that one. Edit: just added some facts about perfect complexes of \O_X-modules.

   Is the definition on this page standard? I’ve only seen the definition for modules over a ring or ringed space and they don’t seem to be in exact agreement with that one.

   Edit: just added some facts about perfect complexes of \O_X-modules.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 2nd 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for adding stuff! Concerning perfection: Hm, [here](http://uk.arxiv.org/abs/0805.0157) on p. 3 it has "finite complex of projective modules", [here](http://lanl.arxiv.org/abs/0801.3904) on p. 2 it has "cofibrant and totally finitely generated", [here](http://books.google.nl/books?id=MS5QSjBX3mcC&pg=PA9&lpg=PA9&dq=%22perfect+chain+complex%22&source=bl&ots=i7r3PCQq-5&sig=lVLuEa0R6e3IpM26oVVLdb4UurA&hl=en&sa=X&ei=VybTUdiPK4PfOKiUgOgN&redir_esc=y#v=onepage&q=%22perfect%20chain%20complex%22&f=false) it has "of finite length, with entries finitely generated and projective". So I guess the nLab entry _[[projective complex]]_ was mainly missing the "finitely generated"-clause. I have added that now (or will have once the server wakes up...). But if you feel energetic, please go ahead and further fine-tune this.

   Thanks for adding stuff!

   Concerning perfection: Hm, here on p. 3 it has “finite complex of projective modules”, here on p. 2 it has “cofibrant and totally finitely generated”, here it has “of finite length, with entries finitely generated and projective”.

   So I guess the nLab entry projective complex was mainly missing the “finitely generated”-clause. I have added that now (or will have once the server wakes up…).

   But if you feel energetic, please go ahead and further fine-tune this.