### Abstract

The following are equivalent for a skeletally small abelian Hornfinite category over a field with enough injectives and each simple object being an epimorphic image of a projective object of finite length. (a) Each indecomposable injective has a simple subobject. (b) The category is equivalent to the category of socle-finitely copresented right comodules over a right semiperfect and right cocoherent coalgebra such that each simple right comodule is socle-finitely copresented. (c) The category has left almost split sequences.

Original language | English (US) |
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Pages (from-to) | 3201-3214 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 357 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2005 |

### Keywords

- Abelian category
- Almost split sequence
- Comodule
- Semiperfect cocoherent coalgebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Abelian categories, almost split sequences, and comodules'. Together they form a unique fingerprint.

## Cite this

Kleiner, M., & Reiten, I. (2005). Abelian categories, almost split sequences, and comodules.

*Transactions of the American Mathematical Society*,*357*(8), 3201-3214. https://doi.org/10.1090/S0002-9947-04-03571-8