{"paper":{"title":"Clifford semigroups and the monoidal Grothendieck construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Elena Caviglia, Graham Manuell, Luca Mesiti, Peter F. Faul","submitted_at":"2026-07-14T16:24:14Z","abstract_excerpt":"Clifford semigroups are known to correspond to functors from a semilattice into the category of groups. We show that this correspondence is an instance of the monoidal Grothendieck construction. Moreover, applying the Grothendieck construction to the functor sending a semilattice L to the functor category [L, Grp] yields the category of all Clifford semigroups. We use this to construct a number of factorisation systems on the category of Clifford monoids. Finally, we prove a general result on taking monoids in a monoidal fibration and apply it to give a correspondence between inverse semirings"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12944","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12944/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}