{"paper":{"title":"Cancelation free formula for the antipode of linearized Hopf monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carolina Benedetti, Nantel Bergeron","submitted_at":"2016-11-05T15:08:55Z","abstract_excerpt":"Many combinatorial Hopf algebras $H$ in the literature are the functorial image of a linearized Hopf monoid $\\bf H$. That is, $H={\\mathcal K} ({\\bf H})$ or $H=\\overline{\\mathcal K} ({\\bf H})$. Unlike the functor $\\overline{\\mathcal K}$, the functor ${\\mathcal K}$ applied to ${\\bf H}$ may not preserve the antipode of ${\\bf H}$. In this case, one needs to consider the larger Hopf monoid ${\\bf L}\\times{\\bf H}$ to get $H={\\mathcal K} ({\\bf H})=\\overline{\\mathcal K}({\\bf L}\\times{\\bf H})$ and study the antipode in ${\\bf L}\\times{\\bf H}$. One of the main results in this paper provides a cancelation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01657","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":""},"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"}