{"paper":{"title":"On weakly negative subcategories, weight structures, and (weakly) approximable 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 V. Bondarko, Sergei V. Vostokov","submitted_at":"2019-07-22T16:37:37Z","abstract_excerpt":"We prove that certain triangulated categories are (weakly) approximable in the sense of A. Neeman. We prove that a triangulated $C$ that is compactly generated by a single object $G$ is weakly approximable if $C(G,G[i])=0$ for $i>1$ (we say that $G$ is weakly negative if this assumption is fulfilled; the case where the equality $C(G,G[1])=0$ is fulfilled as well was mentioned by Neeman himself). Moreover, if $G\\cong \\bigoplus_{0\\le i\\le n}G_i$ and $C(G_i,G_j[1])=0$ whenever $i\\le j$ then $C$ is also approximable.\n  The latter result can be useful since (under a few more additional assumptions)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09412","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"}