{
  "annotation_id": "8c680568-12ac-431a-9c40-787b9d994a5d",
  "date_created": "2026-02-17T05:53:24.066000Z",
  "date_modified": "2026-02-17T05:53:24.066000Z",
  "file_hash": "8213a2ec43af9fa97a8b8f54bc33d2bc7c17417c10478d256b171026f77b095d",
  "private": false,
  "record": {
    "abstract": "In this paper, we introduce monoidal rewriting systems (MRS), an abstraction of string rewriting in which reductions are defined over an arbitrary ambient monoid rather than a free monoid of words. This shift is partly motivated by logic: the class of free monoids is not first-order axiomatizable, so \"working in the free setting\" cannot be treated internally when applying first-order methods to rewriting presentations.\n  To analyze these systems categorically, we define $\\mathbf{NCRS_2}$ as the 2-category of Noetherian Confluent MRS. We then prove the existence of a canonical biadjunction between $\\mathbf{NCRS_2}$ and $\\mathbf{Mon}$.\n  Finally, we classify all Noetherian Confluent MRS that present a given fixed monoid. For this, we introduce Generalized Elementary Tietze Transformations (GETTs) and prove that any two presentations of a monoid are connected by a (possibly infinite) sequence of these transformations, yielding a complete characterization of generating systems up to GETT-equivalence.",
    "arxiv_id": "2601.10564",
    "authors": [
      "Eduardo Magalh\u00e3es"
    ],
    "categories": [
      "cs.FL",
      "cs.LO",
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Rewriting Systems on Arbitrary Monoids",
    "url": "https://arxiv.org/abs/2601.10564",
    "version": "v4"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2e6fc9b1-b028-49e9-be4b-e5b8c336c2b3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}