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arXiv · 2610.20386

The Kaplansky-Walker Lemma for additive categories

Simion Breaz·Cristian Rafiliu
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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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Simion Breaz, Cristian Rafiliu. 2026-10-14. The Kaplansky-Walker Lemma for additive categories. https://arxiv.org/abs/2610.20386

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