Abelian categories, almost split sequences, and comodules

Kleiner, Mark; Reiten, Idun

doi:10.1090/S0002-9947-04-03571-8

Abelian categories, almost split sequences, and comodules
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by Mark Kleiner and Idun Reiten PDF

Trans. Amer. Math. Soc. 357 (2005), 3201-3214 Request permission

Abstract:

The following are equivalent for a skeletally small abelian Hom-finite 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.

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