{"paper":{"title":"Free Banach lattices generated by a lattice and projectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Jos\\'e David Rodr\\'iguez Abell\\'an","submitted_at":"2021-03-15T07:27:36Z","abstract_excerpt":"In this article we deal with the free Banach lattice $FBL\\langle \\mathbb{L} \\rangle$ generated by a lattice $\\mathbb{L}$. We prove that if $FBL\\langle \\mathbb{L} \\rangle$ is projective then $\\mathbb{L}$ has a maximum and a minimum. On the other hand, we show that if $\\mathbb{L}$ has maximum and minimum then $FBL\\langle \\mathbb{L} \\rangle$ is $2$-lattice isomorphic to a $C(K)$-space. As a consequence, $FBL\\langle \\mathbb{L} \\rangle$ is projective if and only if it is lattice isomorphic to a $C(K)$-space with $K$ being an absolute neighborhood retract. As an application, we characterize those li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.08170","kind":"arxiv","version":1},"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/2103.08170/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"}