{"paper":{"title":"A Functorial Link between Quivers and Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.CO","authors_text":"Will Grilliette","submitted_at":"2016-07-30T01:35:00Z","abstract_excerpt":"This paper discusses some issues arising from the category $\\mathfrak{H}$ of hypergraphs, the category $\\mathfrak{M}$ of (undirected) multigraphs, and the topos $\\mathfrak{Q}$ of quivers. First, the natural inclusion of $\\mathfrak{M}$ into $\\mathfrak{H}$ admits a right adjoint functor by deleting all nontraditional edges. Dually, the operations of taking the underlying multigraph of a quiver and taking the associated digraph of a multigraph form an adjoint pair between $\\mathfrak{M}$ and $\\mathfrak{Q}$.\n  On the other hand, neither $\\mathfrak{H}$ nor $\\mathfrak{M}$ is cartesian closed, meaning"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00058","kind":"arxiv","version":4},"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"}