{
  "abstract": "We study the equivariant lifting of cleft extensions of abelian categories and its impact on singularity categories. Specifically, we establish the necessary framework for lifting a cleft extension to a G-equivariant cleft extension. Furthermore, we prove that a restriction functor associated to a cleft extension induces a singular equivalence if and only if its equivariant counterpart does. As a concrete application, we demonstrate that the skew group ring of a $G$-equivariant $θ$-extension is isomorphic to a $\\widehatθ$-extension of the base skew group ring, allowing us to lift singular equivalences for these structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25560",
  "author_total": 1,
  "authors": [
    {
      "name": "Miltiadis Karakikes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hc20yxvn7he6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25560",
  "fulltext_url": null,
  "id": "7hc20yxvn7he6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25560",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7165887142",
  "pdf_url": "https://arxiv.org/pdf/2606.25560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hc20yxvn7he6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.25560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25560"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Equivariant Cleft Extensions and Singular Equivalences",
  "title_text": "Equivariant Cleft Extensions and Singular Equivalences",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/7hc20yxvn7he6",
  "venue": "arXiv",
  "versions": []
}