{"paper":{"title":"Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.CO","authors_text":"Louis Carlier","submitted_at":"2019-03-19T12:36:57Z","abstract_excerpt":"We show that Schmitt's hereditary species induce monoidal decomposition spaces, and exhibit Schmitt's bialgebra construction as an instance of the general bialgebra construction on a monoidal decomposition space. We show furthermore that this bialgebra structure coacts on the underlying restriction-species bialgebra structure so as to form a comodule bialgebra. Finally, we show that hereditary species induce a new family of examples of operadic categories in the sense of Batanin and Markl."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07964","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"}