Vol. 91, No. 2, 1980

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Stable sequences in pre-abelian categories

Yonina S. Cooper

Vol. 91 (1980), No. 2, 263–267
Abstract

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() for an arbitrary sequence E, is in error. We show, however, that (αE)β = α() 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
Milestones
Received: 16 October 1978
Revised: 25 April 1979
Published: 1 December 1980
Authors
Yonina S. Cooper