On the Notion of a SemiAbelian Category in the Se

Authors: Yaroslav Kopylov SvenAke Wegner

Publish Date: 2011/03/25

Volume: 20, Issue: 5, Pages: 531-541

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Abstract

In the sense of Palamodov a preabelian category is semiabelian if for every morphism the natural morphism between the cokernel of its kernel and the kernel of its cokernel is simultaneously a monomorphism and an epimorphism In this article we present several conditions which are all equivalent to semiabelianity First we consider left and right semiabelian categories in the sense of Rump and establish characterizations of these notions via six equivalent properties Then we use these properties to deduce the characterization of semiabelianity Finally we investigate two examples arising in functional analysis which illustrate that the notions of right and left semiabelian categories are distinct and in particular that such categories occur in nature

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