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A note on natural maps of higher extension functors

Published online by Cambridge University Press:  24 October 2008

F. Oort
F. Oort
Affiliation:
Mathematisch Instituut, Nieuwe Achtergracht 121, Amsterdam (C), The Netherlands
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Extract

Hilton and Rees have proved (cf. (1), Theorem 1·3) that every natural map

is induced by a map from A to B (or, Hom (A, B) → Next1,1 (A, B) is surjective). It follows that Ext1 (B, −) and Ext1 (A, −) are naturally isomorphic if and only if A and B are quasi-isomorphic (loc. cit., Theorem 2·6), i.e. if there exist projective objects P, Q and an isomorphism . One can ask whether these theorems remain true for higher extension functors.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 283 - 286
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCE

(1)Hilton, P. J., and Rees, D., Natural maps of extension functors and a theorem of R. G. Swan. Proc. Cambridge Philos. Soc. 57 (1961), 489–502.CrossRefGoogle Scholar