### 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) |
---|---|

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 2005 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*357*(8), 3201-3214. https://doi.org/10.1090/S0002-9947-04-03571-8

**Abelian categories, almost split sequences, and comodules.** / Kleiner, Mark; Reiten, Idun.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 357, no. 8, pp. 3201-3214. https://doi.org/10.1090/S0002-9947-04-03571-8

}

TY - JOUR

T1 - Abelian categories, almost split sequences, and comodules

AU - Kleiner, Mark

AU - Reiten, Idun

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

KW - Abelian category

KW - Almost split sequence

KW - Comodule

KW - Semiperfect cocoherent coalgebra

UR - http://www.scopus.com/inward/record.url?scp=23244462231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23244462231&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-04-03571-8

DO - 10.1090/S0002-9947-04-03571-8

M3 - Article

AN - SCOPUS:23244462231

VL - 357

SP - 3201

EP - 3214

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 8

ER -