Abelian categories, almost split sequences, and comodules

Mark Kleiner, Idun Reiten

Research output: Contribution to journalArticle

9 Scopus citations

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 languageEnglish (US)
Pages (from-to)3201-3214
Number of pages14
JournalTransactions of the American Mathematical Society
Volume357
Issue number8
DOIs
StatePublished - 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