Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-21T06:48:33.628Z Has data issue: false hasContentIssue false
  • English
  • Français

A lemma in homological algebra

Published online by Cambridge University Press:  24 October 2008

G. M. Kelly
G. M. Kelly
Affiliation:
Tulane University, Louisiana
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the development of homological algebra, one has to prove at some point that, in defining the derived functors of ⊗ and of Hom, it makes no difference whether we resolve both variables or only one of them. Taking ⊗ ( = ⊗R) as a typical example, what has to be proved is

(A) If the complex F is projective, or even flat, as a right R-module, and if f: P → A is a projective resolution of the left R-module A, then

is an isomorphism.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 49 - 52
Copyright
Copyright © Cambridge Philosophical Society 1965

References

REFERENCES

(1)Cartan, H. and Eilenberg, S.Homological algebra (Princeton, 1956).Google Scholar
(2)Dold, A.Zur Homotopietheorie der Kettenkomplexe. Math. Ann. 140 (1960), 278–298.CrossRefGoogle Scholar
(3)Godement, R.Théorie des faisceaux (Paris, 1958).Google Scholar
(4)MacLane, S.Homology (New York, 1963).CrossRefGoogle Scholar