PreprintCC BY 4.0arXiv
The Kaplansky-Walker Lemma for additive categories
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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BibTeX
@misc{breaz2026kaplanskywalker,
title = {{The Kaplansky-Walker Lemma for additive categories}},
author = {Simion Breaz and Cristian Rafiliu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20386},
eprint = {2610.20386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Kaplansky-Walker Lemma for additive categories
AU - Simion Breaz
AU - Cristian Rafiliu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20386
UR - https://arxiv.org/abs/2610.20386
AB - 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.
ER -