{
  "abstract": "Let Q be an integral, commutative quantale with a completely distributive underlying lattice. It is known that there is a one-to-one correspondence between the category of quantale-valued tolerance spaces and tolerance-preserving mappings, denoted by Q-TOL, and the category of quantale-valued tolerance convergence spaces and continuous mappings, denoted by Q-TOLCONV. Our motivations in this article include introducing Q-tolerance structures on quantale-valued tolerance function spaces as well as on quantale-valued tolerance convergence function spaces. We prove that the category Q-TOLCONV and the category Q-TOLCONVGRP, consisting of quantale-valued tolerance convergence groups, are topological categories, and we provide examples of natural transformations in the category Q-TOL. Moreover, we show that both categories are cartesian closed; in particular, for the category Q-TOLCONV, we present a categorical proof of cartesian closedness via an adjoint functor. Furthermore, we study quantale-valued tolerance convergence function space structures on groups of homeomorphisms, where the homeomorphism group serves as a canonical framework for analyzing the compatibility of quantale-valued convergence with topological symmetries. This analysis clarifies how quantale-valued convergence interacts with algebraic symmetry and provides the structural foundation for our final result that quantale-valued tolerance convergence groups are group objects in Q-TOLCONV.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "T. M. G. Ahsanullah",
      "orcid": "0000-0002-3012-566X"
    },
    {
      "affs": [
        0
      ],
      "name": "Jawaher Al-Mufarrij",
      "orcid": "0000-0002-5645-0428"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5brv98f6c3cxf.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15110823",
  "fulltext_url": null,
  "id": "5brv98f6c3cxf",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/11/823",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/5brv98f6c3cxf.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:47Z",
      "native_id": "10.3390/axioms15110823",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/11/823"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Quantale-Valued Tolerance Convergence Function Spaces: Topological and Cartesian-Closed Categorical Perspectives",
  "title_text": "Quantale-Valued Tolerance Convergence Function Spaces: Topological and Cartesian-Closed Categorical Perspectives",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T00:21:04Z",
  "url": "https://research.draconitic.com/paper/5brv98f6c3cxf",
  "venue": "Axioms",
  "versions": []
}