On the Notion of a Semi-Abelian Category in the Sense of Palamodov

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.

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Correspondence to Sven-Ake Wegner.

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Kopylov, Y., Wegner, SA. On the Notion of a Semi-Abelian Category in the Sense of Palamodov. Appl Categor Struct 20, 531–541 (2012). https://doi.org/10.1007/s10485-011-9249-0

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Keywords

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

Mathematics Subject Classifications (2010)

  • Primary 18A20; Secondary 46M18