{"paper":{"title":"Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Gabriella B\\\"ohm","submitted_at":"2016-11-16T06:07:03Z","abstract_excerpt":"We associate, in a functorial way, a monoidal bicategory $\\mathsf{Span}| \\mathcal V$ to any monoidal bicategory $\\mathcal V$. Two examples of this construction are of particular interest: Hopf polyads (due to Brugui\\`eres) can be seen as Hopf monads in $\\mathsf{Span}| \\mathsf{Cat}$ while Hopf group monoids in a braided monoidal category $V$ (in the spirit of Turaev and Zunino), and Hopf categories over $V$ (by Batista, Caenepeel and Vercruysse) both turn out to be Hopf monads in $\\mathsf{Span}| V$. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05157","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}