{"paper":{"title":"Relatively divisible and relatively flat objects in exact categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Derya Kesk\\.in T\\\"ut\\\"unc\\\"u, Septimiu Crivei","submitted_at":"2018-10-27T13:02:30Z","abstract_excerpt":"We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair $(\\mathcal{A},\\mathcal{B})$ in an exact category $\\mathcal{C}$, $\\mathcal{A}$ coincides with the class of relatively flat objects of $\\mathcal{C}$ for some relative projectively generated exact structure, while $\\mathcal{B}$ coincides with the class of relatively divisible objects of $\\mathcal{C}$ for some relative injectively generated exact structure. We exhibit Galois connections between relative cotorsion pairs, relative projectively generat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11637","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":""},"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"}