{"paper":{"title":"Gabi-Monads","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CT","authors_text":"Paolo Saracco, Sebastian Halbig, Tony Zorman","submitted_at":"2026-07-30T08:25:35Z","abstract_excerpt":"We study gabi-monads on skew-closed categories, extending the gabi-algebras of Berger, the second author, and Vercruysse beyond the linear case. Our main reconstruction theorem identifies gabi-monad structures on a monad with skew-closed structures on its Eilenberg--Moore category for which the canonical forgetful functor is strict closed. We compare this notion with closed monads in the sense of Kock, showing that in representation-theoretic cases these notions are quite different. On closed monoidal categories, every left Hopf monad is a normal gabi-monad, but the converse fails in general. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27846","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/2607.27846/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"}