Quantification in Double-Categorical Database Schemas

[2608.00913] Quantification in Double-Categorical Database Schemas Skip to main content Search Submit Donate Log in Mathematics > Category Theory arXiv:2608.00913 (math) [Submitted on 2 Aug 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Quantification in Double-Categorical Database Schemas Authors: Michael Lambert View PDF Abstract: Double-categorical database schemas are enriched with universal quantification in the form of right adjoints to substitution. This allows phrasing of the important query, relational division. It is shown that such right adjoints together with suitable tabulators interpret modal operators, provide cartesian closed structure, and, when combined with global cocartesian structure, interpret first-order predicate logic and thus description logic. These structures are applied throughout to querying and optimization. It is seen, for example, that Frobenius reciprocity and Beck-Chevalley hold in any suitably structured double database schema and that these provide pushdown optimization rules. Such optimization rules are thus provably error-free as a property of the schema. Likewise, negation queries are derived from cocartesian and local implication structure. Comments: 46 pages, 1 figure Subjects: Category Theory (math.CT) ; Databases (cs.DB); Logic in Computer Science (cs.LO) MSC classes: 18N10 (Primary), 18N45, 68P15 (Secondary) Cite as: arXiv:2608.00913 [math.CT] (or arXiv:2608.00913v2 [math.CT] for this version) https://doi.org/10.48550/arXiv.2608.00913 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Michael Lambert [ view email ] [v1] Sun, 2 Aug 2026 00:35:19 UTC (67 KB) [v2] Sat, 22 Aug 2026 00:48:03 UTC (66 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.CT < prev | next > new | recent | 2026-08 Change to browse by: cs cs.DB cs.LO math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

Related documents

• Quantification in Double-Categorical Database Schemas#670713
• Multiset semantics in SPARQL, Relational Algebra and Datalog#155425
• Dinaturality for Double Categories#1155132
• A two-categorical Snake Lemma#974005
• 3D Bar Graph#1042286