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ON KRULL–SCHMIDT FINITELY ACCESSIBLE CATEGORIES
Published online by Cambridge University Press: 01 April 2011
Abstract
Let 𝒞 be a finitely accessible additive category with products, and let (Ui)i∈I be a family of representative classes of finitely presented objects in 𝒞 such that each object Ui is pure-injective. We show that 𝒞 is a Krull–Schmidt category if and only if every pure epimorphic image of the objects Ui is pure-injective.
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
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