Monoidal Quantaloids

[2504.18266] Monoidal Quantaloids Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Category Theory arXiv:2504.18266 (math) [Submitted on 25 Apr 2025 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: Monoidal Quantaloids Authors: Gejza Jenča , Bert Lindenhovius View a PDF of the paper titled Monoidal Quantaloids, by Gejza Jen\v{c}a and Bert Lindenhovius View PDF HTML (experimental) Abstract: We investigate how to add a symmetric monoidal structure to quantaloids in a compatible way. In particular, dagger compact quantaloids turn out to have properties that are similar to the category Rel of sets and binary relations. Examples of such quantaloids are the category qRel of quantum sets and binary relations, and the category V-Rel of sets and binary relations with values in a commutative quantale V. For both examples, the process of internalization structures is of interest. Discrete quantization, a process of generalization of mathematical structures to the noncommutative setting can be regarded as the process of internalizing these structures in qRel, whereas fuzzification, the process of introducing degrees of truth or membership to concepts that are traditionally considered either true or false, can be regarded as the process of internalizing structures in V-Rel. Hence, we investigate how to internalize power sets and preordered structures in dagger compact quantaloids. Comments: 78 pages, 15 figures. Substantial revision based on reviewer feedback Subjects: Category Theory (math.CT) ; Mathematical Physics (math-ph); Operator Algebras (math.OA) MSC classes: 18D20, 18M40, 06F07 Cite as: arXiv:2504.18266 [math.CT] (or arXiv:2504.18266v3 [math.CT] for this version) https://doi.org/10.48550/arXiv.2504.18266 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bert Lindenhovius [ view email ] [v1] Fri, 25 Apr 2025 11:26:21 UTC (81 KB) [v2] Thu, 18 Dec 2025 18:38:15 UTC (122 KB) [v3] Thu, 9 Apr 2026 09:21:53 UTC (121 KB) Full-text links: Access Paper: View a PDF of the paper titled Monoidal Quantaloids, by Gejza Jen\v{c}a and Bert Lindenhovius View PDF HTML (experimental) TeX Source view license Current browse context: math.CT < prev | next > new | recent | 2025-04 Change to browse by: math math-ph math.MP math.OA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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