Derived Functor SemiExt

  • Leonid PositselskiEmail author
  • Sergey Arkhipov
  • Dmitriy Rumynin
Part of the Monografie Matematyczne book series (MONOGRAFIE, volume 70)


Let A be an exact category in which all infinite products exist and the functors of infinite product are exact. A complex C over A is called Italic if it belongs to the minimal triangulated subcategory Acycl ctr (A) of the homotopy category Hot(A) containing all the total complexes of exact triples ′K → K → ″K of complexes over A and closed under infinite products. Any contraacyclic complex is acyclic. It follows from the next lemma that any acyclic complex bounded from above is contraacyclic.


Full Subcategory Abelian Category Total Complex Arbitrary Complex Triangulate Category 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Leonid Positselski
    • 1
    Email author
  • Sergey Arkhipov
    • 2
  • Dmitriy Rumynin
    • 3
  1. 1.Sector of Algebra and Number TheoryInstitute for Information Transmission ProblemsMoscowRussia
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada
  3. 3.Mathematics DepartmentUniversity of WarwickCoventryUK

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