{"paper":{"title":"The existence of UFO implies projectively universal morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.OA"],"primary_cat":"math.FA","authors_text":"Marek Balcerzak, Tomasz Kania","submitted_at":"2022-08-06T20:32:40Z","abstract_excerpt":"Let $\\mathcal C$ be a concrete category. We prove that if $\\mathcal{C}$ admits a universally free object $\\mathsf F$, then there is a projectively universal morphism $u\\colon \\mathsf F\\to \\mathsf F$, i.e., a morphism $u$ such that for any $B\\in \\mathcal{C}$ and $\\tau\\in {\\rm Mor}(B)$ there exists an epimorphism $\\pi\\in {\\rm Mor}(\\mathsf F, B)$ such that $\\pi \\tau = u \\pi$. This builds upon and extends various ideas by Darji and Matheron (Proc. Am. Math. Soc. 145 (2017)) who proved such a result for the category of separable Banach spaces with contractive operators as well as certain classes of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.03579","kind":"arxiv","version":2},"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/2208.03579/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"}