Satellites and Homology

  • P. J. Hilton
  • U. Stammbach
Part of the Graduate Texts in Mathematics book series (GTM, volume 4)


In Chapters VI and VII we gave “concrete” applications of the theory of derived functors established in Chapter IV, namely to the category of groups and the category of Lie algebras over a field K. In this chapter our first purpose is to broaden the setting in which a theory of derived functors may be developed. This more general theory is called relative homological algebra, the relativization consisting of replacing the class of all epimorphisms (monomorphisms) by a suitable subclass in defining the notion of projective (injective) object. An important example of such a relativization, which we discuss explicitly, consists in taking, as our projective class of epimorphisms in the category M Λ of Λ-modules, those epimorphisms which split as abelian group homomorphisms.


Abelian Group Exact Sequence Spectral Sequence Natural Transformation Additive Functor 
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Copyright information

© Springer Science+Business Media New York 1971

Authors and Affiliations

  • P. J. Hilton
    • 1
    • 2
  • U. Stammbach
    • 3
  1. 1.Battelle Memorial InstituteSeattleUSA
  2. 2.Department of Mathematics and StatisticsCase Western Reserve UniversityClevelandUSA
  3. 3.Mathematisches InstitutEidgenössische Technische HochschuleZurichSwitzerland

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