Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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.