{"paper":{"title":"On the weight lifting property for localizations of triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.KT","authors_text":"Mikhail Bondarko, Vladimir Sosnilo","submitted_at":"2015-10-12T19:24:08Z","abstract_excerpt":"As we proved earlier, for a triangulated category $\\underline{C}$ endowed with a weight structure $w$ and a triangulated subcategory $\\underline{D}$ of $\\underline{C}$ (strongly) generated by cones of a set of morphisms $S$ in the heart $\\underline{Hw}$ of $w$ there exists a weight structure $w'$ on the Verdier quotient $\\underline{C}'=\\underline{C}/\\underline{D}$ such that the localization functor $\\underline{C} \\to \\underline{C}'$ is weight-exact (i.e., \"respects weights\"). The goal of this paper is to find conditions ensuring that for any object of $\\underline{C}'$ of non-negative (resp. no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03403","kind":"arxiv","version":3},"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"}