{"paper":{"title":"On equivariant triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexey Elagin","submitted_at":"2014-03-27T13:45:51Z","abstract_excerpt":"Consider a finite group $G$ acting on a triangulated category $\\mathcal T$. In this paper we investigate triangulated structure on the category $\\mathcal T^G$ of $G$-equivariant objects in $\\mathcal T$. We prove (under some technical conditions) that such structure exists. Supposed that an action on $\\mathcal T$ is induced by a DG-action on some DG-enhancement of $\\mathcal T$, we construct a DG-enhancement of $\\mathcal T^G$. Also, we show that the relation \"to be an equivariant category with respect to a finite abelian group action\" is symmetric on idempotent complete additive categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7027","kind":"arxiv","version":2},"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"}