{"paper":{"title":"A bicategory of decorated cospans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Kenny Courser","submitted_at":"2016-05-25T23:07:59Z","abstract_excerpt":"If $\\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has developed a theory of \"decorated\" cospans, which are cospans in $\\mathbf{C}$ equipped with extra structure. This extra structure arises from a lax symmetric monoidal functor $F \\colon \\mathbf{C} \\to \\mathbf{D}$; we use this functor to \"decorate\" each cospan with apex $N \\in \\mathbf{C}$ with an element of $F(N)$. Using a result of Shulman, we show that when $\\mathbf{C}$ has finite colimits, decorated co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08100","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"}