Derived Functor SemiTor

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


A complex C over an exact category [28] A is called exact if it is composed of exact triples Zi → Ci → Zi+1 in A. A complex over A is called acyclic if it is homotopy equivalent to an exact complex (or equivalently, if it is a direct summand of an exact complex). Acyclic complexes form a thick subcategory Acycl(A) of the homotopy category Hot(A) of complexes over A. All acyclic complexes over A are exact if and only if A contains images of idempotent endomorphisms [69].


Full Subcategory Coderived Category Abelian Category Tensor Category Total Complex 
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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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