{"paper":{"title":"A generalization of Gabriel's Galois covering functors and derived equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hideto Asashiba","submitted_at":"2008-07-29T17:02:58Z","abstract_excerpt":"Let $G$ be a group acting on a category $\\mathcal{C}$. We give a definition for a functor $F\\colon \\mathcal{C} \\to \\mathcal{C}'$ to be a $G$-covering and three constructions of the orbit category $\\mathcal{C}/G$, which generalizes the notion of a Galois covering of locally finite-dimensional categories with group $G$ whose action on $\\mathcal{C}$ is free and locally bonded defined by Gabriel. Here $\\mathcal{C}/G$ is defined for any category $\\mathcal{C}$ and we do not require that the action of $G$ is free or locally bounded. We show that a $G$-covering is a universal \"$G$-invariant\" functor a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4706","kind":"arxiv","version":7},"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"}