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Stable sequences in
pre-abelian categories
Yonina S. Cooper |
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Vol. 91 (1980), No. 2, 263–267
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Abstract |
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In the Pacific Journal of Mathematics, 71 (1977), Richman and Walker gave a natural definition for Ext in an arbitrary pre-abelian category. Their Theorem 4, which states that (αE)β = α(Eβ) for an arbitrary sequence E, is in error. We show, however, that (αE)β = α(Eβ) does hold for a stable exact sequence. Without Theorem 4, the crucial step in their theory is showing that αE is stable if E is stable. We prove this. Consequently, the theory of Richman and Walker for Ext in a pre-abelian category is valid. |
Mathematical Subject Classification 2000
Primary: 18E05
Secondary: 18G15
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Milestones
Received: 16 October 1978
Revised: 25 April 1979
Published: 1 December 1980
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Authors |
| Yonina S. Cooper | |
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