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Derived Functor SemiTor

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

Abstract

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].

Keywords

Full Subcategory Coderived Category Abelian Category Tensor Category Total Complex 
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 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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