A note on natural maps of higher extension functors
Published online by Cambridge University Press: 24 October 2008
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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