{"paper":{"title":"The Catalan simplicial set II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mitchell Buckley","submitted_at":"2014-11-26T04:40:30Z","abstract_excerpt":"The Catalan simplicial set $\\mathbb{C}$ is known to classify skew-monoidal categories in the sense that a map from $\\mathbb{C}$ to a suitably defined nerve of $\\mathrm{Cat}$ is precisely a skew-monoidal category \\cite{Catalan1}. We extend this result to the case of skew monoidales internal to any monoidal bicategory $\\mathcal{B}$. We then show that monoidal bicategories themselves are classified by maps from $\\mathbb{C}$ to a suitably defined nerve of $\\mathrm{Bicat}$ and extend this result to obtain a definition of skew-monoidal bicategory that aligns with existing theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7107","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"}