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A lemma in homological algebra

Published online by Cambridge University Press:  24 October 2008

G. M. Kelly
G. M. Kelly
Affiliation:
Tulane University, Louisiana
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Extract

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

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References

REFERENCES

(1)Cartan, H. and Eilenberg, S.Homological algebra (Princeton, 1956).Google Scholar
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(3)Godement, R.Théorie des faisceaux (Paris, 1958).Google Scholar
(4)MacLane, S.Homology (New York, 1963).CrossRefGoogle Scholar