## 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 language | English |
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Pages (from-to) | 531-541 |

Number of pages | 11 |

Journal | Applied Categorical Structures |

Volume | 20 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Oct 2012 |