{
  "abstract": "We present some theoretical aspects of the categories of global and partial group actions of topological groups on topological spaces, denoted by G-ActTop and G-pActTop, respectively. We construct topological partial actions on products and disjoint unions of topological spaces, and G-pinvariant subspaces. Furthermore, we provide an adequate definition of congruence (G-pcongruence), which enables the construction of quotient objects in the category of topological partial actions. In addition, we associate a special G-pcongruence to each pair of strong G-pmorphisms. Then, we study products, co-products, equalizers, co-equalizers, pullbacks, and pushouts in the category G-pActTop. We find that the category of topological partial actions is finitely complete and contains a co-complete subcategory. Finally, we show that the relationship between a topological partial action and its enveloping action is functorial. As a consequence, we obtain that the categorical product in G-ActTop coincides with the categorical product in G-pActTop. Moreover, the envelope of a co-product in G-pActTop is given by the co-product of the respective envelopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00363",
  "author_total": 2,
  "authors": [
    {
      "name": "Jesús Ávila"
    },
    {
      "name": "Fabián Molina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7j73hd257d3dn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00363",
  "fulltext_url": null,
  "id": "7j73hd257d3dn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00363",
  "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.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7j73hd257d3dn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Some Constructions in the Category of Topological Partial Actions",
  "title_text": "Some Constructions in the Category of Topological Partial Actions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/7j73hd257d3dn",
  "venue": "arXiv",
  "versions": []
}