On the notion of a semi-abelian category in the sense of Palamodov

Yaroslav Kopylov, Sven Ake Wegner

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In the sense of Palamodov, a preabelian category is semi-abelian 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 semi-abelianity. First we consider left and right semi-abelian 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 semi-abelianity. Finally, we investigate two examples arising in functional analysis which illustrate that the notions of right and left semi-abelian categories are distinct and in particular that such categories occur in nature.

Original languageEnglish
Pages (from-to)531-541
Number of pages11
JournalApplied Categorical Structures
Volume20
Issue number5
DOIs
Publication statusPublished - Oct 2012
Externally publishedYes

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Semi-abelian Category
Morphism
kernel
Monomorphism
Epimorphism
Functional analysis
Functional Analysis
Deduce
Distinct

Keywords

  • Category of bornological spaces
  • Preabelian category
  • Quasi-abelian category
  • Semi-abelian category

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

On the notion of a semi-abelian category in the sense of Palamodov. / Kopylov, Yaroslav; Wegner, Sven Ake.

In: Applied Categorical Structures, Vol. 20, No. 5, 10.2012, p. 531-541.

Research output: Contribution to journalArticle

Kopylov, Yaroslav ; Wegner, Sven Ake. / On the notion of a semi-abelian category in the sense of Palamodov. In: Applied Categorical Structures. 2012 ; Vol. 20, No. 5. pp. 531-541.
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