{"paper":{"title":"The naive approach for constructing the derived category of a $d$-abelian category fails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gustavo Jasso, Julian K\\\"ulshammer","submitted_at":"2016-04-12T16:28:53Z","abstract_excerpt":"Let $k$ be a field. In this short note we give an example of a $2$-abelian $k$-category, realized as a $2$-cluster-tilting subcategory of the category $\\operatorname{mod}\\,A$ of finite dimensional (right) $A$-modules over a finite dimensional $k$-algebra $A$, for which the naive idea for constructing its \"bounded derived category\" as $2$-cluster-tilting subcategory of the bounded derived category of $\\operatorname{mod}\\,A$ cannot work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03473","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"}