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manuscripta mathematica

, Volume 67, Issue 1, pp 379–417 | Cite as

Chain complexes and stable categories

  • Bernhard Keller
Article

Abstract

Under suitable assumptions, we extend the inclusion of an additive subcategory\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}} \subset \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}\) (=stable category of an exact category with enough injectives) to anS-functor [15]\(\mathcal{H}_{0]} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}} \to \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}\), where\(\mathcal{H}_{0]} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}}\) is the homotopy category of chain complexes concentrated in positive degrees. We thereby obtain a new proof for the key result of J. Rickard’s ‘Morita theory for Derived categories’ [17] and a sharpening of a theorem of Happel [12,10.10] on the ‘module-theoretic description’ of the derived category of a finite-dimensional algebra.

Keywords

Exact Sequence Short Exact Sequence Direct Limit Full Subcategory Abelian Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Bernhard Keller
    • 1
  1. 1.ETH-Zentrum, G 28.2ZurichSwitzerland

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