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ON KRULL–SCHMIDT FINITELY ACCESSIBLE CATEGORIES

Published online by Cambridge University Press:  01 April 2011

SEPTIMIU CRIVEI*
Affiliation:
Faculty of Mathematics and Computer Science, ‘Babeş-Bolyai’ University, Str. M. Kogălniceanu 1, 400084 Cluj-Napoca, Romania (email: [email protected])
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Abstract

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Let 𝒞 be a finitely accessible additive category with products, and let (Ui)iI 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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