{"paper":{"title":"Decorated Cospans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Brendan Fong","submitted_at":"2015-02-03T14:26:36Z","abstract_excerpt":"Let $\\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\\mathcal D, \\otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $F: (\\mathcal C,+) \\to (\\mathcal D, \\otimes)$, and of producing a strong monoidal functor between such categories from a monoidal natural transformation between such functors. The objects of these categories, our so-called `decorated cospan categories', are simply the objects of $\\mathcal C$, while the morphisms are pairs comprising a cospan $X \\rightarr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00872","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":""},"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"}