{"paper":{"title":"From objects to diagrams for ranges of functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GM","math.LO","math.RA"],"primary_cat":"math.CT","authors_text":"Friedrich Wehrung (LMNO), Pierre Gillibert (MFF-UK)","submitted_at":"2010-03-25T10:44:04Z","abstract_excerpt":"Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for \"many\" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to transfer this statement to diagrams of A. These diagrams are all indexed by posets in which every principal ideal is a join-semilattice and the set of all upper bounds of any finite subset is a finitely generated upper subset. Various consequences follow, in particular: (1) The Gr\\\"atzer-Schmidt Theorem, which states that every algebraic lattice is isomorphic t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4850","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":""},"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"}