{"paper":{"title":"When an abelian category with a tilting object is equivalent to a module category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Alberto Tonolo, Francesca Mantese, Riccardo Colpi","submitted_at":"2010-11-24T11:40:23Z","abstract_excerpt":"An abelian category with arbitrary coproducts and a small projective generator is equivalent to a module category \\cite{Mit}. A tilting object in a abelian category is a natural generalization of a small projective generator. Moreover, any abelian category with a tilting object admits arbitrary coproducts \\cite{CGM}. It naturally arises the question when an abelian category with a tilting object is equivalent to a module category. By \\cite{CGM} the problem simplifies in understanding when, given an associative ring $R$ and a faithful torsion pair $(\\X,\\Y)$ in the category of right $R$-modules,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5345","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"}