Abstract
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 ###mΛ of Λ-modules, those epimorphisms which split as abelian group homomorphisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hilton, P.J., Stammbach, U. (1997). Satellites and Homology. In: A Course in Homological Algebra. Graduate Texts in Mathematics, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8566-8_10
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8566-8_10
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6438-5
Online ISBN: 978-1-4419-8566-8
eBook Packages: Springer Book Archive