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.
CITATION STYLE
Kleiner, M., & Reiten, I. (2004). 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
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