{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20386",
  "author_total": 2,
  "authors": [
    {
      "name": "Simion Breaz"
    },
    {
      "name": "Cristian Rafiliu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjjzsqf09fbtz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20386",
  "fulltext_url": null,
  "id": "cjjzsqf09fbtz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20386",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7222347609",
  "pdf_url": "https://arxiv.org/pdf/2610.20386",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjjzsqf09fbtz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20386",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20386"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Kaplansky-Walker Lemma for additive categories",
  "title_text": "The Kaplansky-Walker Lemma for additive categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cjjzsqf09fbtz",
  "venue": "arXiv",
  "versions": []
}