{"paper":{"title":"Equivalences of Graded Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Cain Edie-Michell","submitted_at":"2017-11-02T08:17:28Z","abstract_excerpt":"We further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the $\\mathcal{C}$-based equivalences between two $G$-graded extensions of $\\mathcal{C}$. The main result of this paper (which follows from this classification) shows that there is an action of the group $\\operatorname{Aut}(G)\\times \\operatorname{Aut}_\\otimes(\\mathcal{C})$ on the set of all $G$-graded extensions of $\\mathcal{C}$, and further, any two extensions in the same orbit of this action are monoidally equivalent. As a warm up for the proof of our classification result we reprove the classification o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00645","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"}