Abelian categories, almost split sequences, and comodules

Mark Kleiner, Idun Reiten

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 2005

Fingerprint

Almost Split Sequence
Abelian Category
Comodule
Socle
Coalgebra
Injective
Object

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Transactions of the American Mathematical Society, Vol. 357, No. 8, 08.2005, p. 3201-3214.

Research output: Contribution to journalArticle

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