Clifford semigroups and the monoidal Grothendieck construction

[2607.12944] Clifford semigroups and the monoidal Grothendieck construction Skip to main content Search Submit Donate Log in Mathematics > Category Theory arXiv:2607.12944 (math) [Submitted on 14 Jul 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Clifford semigroups and the monoidal Grothendieck construction Authors: Elena Caviglia , Peter F. Faul , Graham Manuell , Luca Mesiti View PDF Abstract: We show that the monoidal Grothendieck construction can be applied to recover the known structure theorem for Clifford monoids, which states that they correspond to functors from a semilattice into the category of groups. Furthermore, we capture the category of Clifford monoids itself as a Grothendieck construction of the functor sending a semilattice L to the functor category [L, Grp] and use this to construct a number of factorisation systems on this category. Finally, we prove a general result on taking monoids in a monoidal fibration and apply it to establish a correspondence between inverse semirings and lax monoidal functors from an idempotent semiring into the category of abelian groups. Comments: 32 pages, a number of minor improvements Subjects: Category Theory (math.CT) ; Rings and Algebras (math.RA) MSC classes: 20M50, 18D30, 20M18, 16Y60, 18M05 Cite as: arXiv:2607.12944 [math.CT] (or arXiv:2607.12944v2 [math.CT] for this version) https://doi.org/10.48550/arXiv.2607.12944 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Graham Manuell [ view email ] [v1] Tue, 14 Jul 2026 16:24:14 UTC (31 KB) [v2] Wed, 26 Aug 2026 21:38:07 UTC (34 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.CT < prev | next > new | recent | 2026-07 Change to browse by: math math.RA 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)

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