{
  "abstract": "For categories, being balanced (meaning that every arrow that is both epic and monic is an isomorphism) can be regarded as a strong tameness property which plays an important role, for example, in algebra and logic. We study the problem of associating a balanced companion category, called a \\emph{Beth companion}, to a locally finitely presentable category (equivalently, the category of models of a finitary essentially algebraic theory). We show that, if it exists, the Beth companion is unique and can be described in terms of \\emph{saturated} objects. Under additional assumptions, we prove that Beth companions can be computed as orthogonality classes, and admit a syntactic presentation via Gabriel--Ulmer duality. Furthermore, we establish conditions for the transfer of properties from a category to its Beth companion. A number of examples of categories that do or do not admit a Beth companion are provided. In particular, we show that the category of commutative rings does not admit a Beth companion, and employ Pierce sheaf representations to describe the Beth companion of other classes of rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03601",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Di Liberti"
    },
    {
      "name": "Luca Reggio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d1rahrt2mgwy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03601",
  "fulltext_url": null,
  "id": "5d1rahrt2mgwy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03601",
  "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"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7208715751",
  "pdf_url": "https://arxiv.org/pdf/2609.03601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d1rahrt2mgwy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.03601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03601"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Beth companions of finitary essentially algebraic theories",
  "title_text": "Beth companions of finitary essentially algebraic theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5d1rahrt2mgwy",
  "venue": "arXiv",
  "versions": []
}