{
  "abstract": "E-graphs are a powerful algorithmic technique for automated equational reasoning but have resisted a conceptual understanding independent of issues of presentation and implementation. We propose an operational semantics for e-graphs based on the fundamental category-theoretic concepts of diagrams, limits, and initial functors. We illustrate the formalism through numerous example calculations and establish its soundness and completeness. Technical prerequisites are kept to a minimum in the main text; less standard elements of the mathematical theory are developed in two appendices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05924",
  "author_total": 1,
  "authors": [
    {
      "name": "Evan Patterson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csnrr82swnt24.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05924",
  "fulltext_url": null,
  "id": "csnrr82swnt24",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05924",
  "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",
      "cs.LO"
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    [
      "arxiv",
      "math.CT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csnrr82swnt24.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "How to prove equations using diagrams: A categorical and operational semantics for e-graphs",
  "title_text": "How to prove equations using diagrams: A categorical and operational semantics for e-graphs",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/csnrr82swnt24",
  "venue": "arXiv",
  "versions": []
}