Quotients-comprehensions duality in relational doctrines

[2608.15199] Quotients-comprehensions duality in relational doctrines Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Category Theory arXiv:2608.15199 (math) [Submitted on 15 Aug 2026] Title: Quotients-comprehensions duality in relational doctrines Authors: Francesco Dagnino , Fabio Pasquali View a PDF of the paper titled Quotients-comprehensions duality in relational doctrines, by Francesco Dagnino and Fabio Pasquali View PDF HTML (experimental) Abstract: We establish a duality between quotients and comprehensions in relational doctrines, a class of indexed posets modelling (a minimal fragment of) the calculus of relations. We show that every relational doctrine determines an ``opposite" relational doctrine and that one has quotients if and only if the other has comprehensions. This duality extends to the 2-categorical level, yielding a 2-dual isomorphism between the 2-categories of relational doctrines with quotients and that with comprehensions, allowing to derive results on relational doctrines with comprehensions from their dual counterparts for quotients, and viceversa. We also study the interaction between quotients and comprehensions and their relative completions, giving sufficient conditions for the induced 2-monads to be composable, \ie sufficient conditions ensuring that applying both the completions, the second one preserves the properties added by the first one. Subjects: Category Theory (math.CT) ; Logic (math.LO) Cite as: arXiv:2608.15199 [math.CT] (or arXiv:2608.15199v1 [math.CT] for this version) https://doi.org/10.48550/arXiv.2608.15199 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Francesco Dagnino [ view email ] [v1] Sat, 15 Aug 2026 12:31:13 UTC (49 KB) Full-text links: Access Paper: View a PDF of the paper titled Quotients-comprehensions duality in relational doctrines, by Francesco Dagnino and Fabio Pasquali View PDF HTML (experimental) TeX Source view license Current browse context: math.CT < prev | next > new | recent | 2026-08 Change to browse by: math math.LO 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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