The Kaplansky-Walker Lemma for additive categories
Simion Breaz, Cristian Rafiliu
Abstract
We establish a Kaplansky-Walker type lemma for idempotent complete additive categories with direct sums. It will be used in compactly generated triangulated categories to provide a version of Kaplansky's theorem on projective modules and an isomorphism-refinement result for direct sums of countable objects.
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