{"paper":{"title":"Polynomials as spans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Ross Street","submitted_at":"2019-03-10T00:06:35Z","abstract_excerpt":"The paper defines polynomials in a bicategory $\\mathscr{M}$. Polynomials in bicategories $\\mathrm{Spn}\\mathscr{C} \\ $ of spans in a finitely complete category $\\mathscr{C} \\ $ agree with polynomials in $\\mathscr{C} \\ $ as defined by Nicola Gambino and Joachim Kock, and by Mark Weber. When $\\mathscr{M}$ is \\textit{calibrated}, we obtain another bicategory $\\mathrm{Poly}\\mathscr{M}$. We see that polynomials in $\\mathscr{M}$ have representations as pseudofunctors $\\mathscr{M}^{\\mathrm{op}}\\to \\mathrm{Cat}$. Calibrations are produced for the bicategory of relations in a regular category and for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03890","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.03890/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}