{"paper":{"title":"A Note on Braided $T$-categories over Monoidal Hom-Hopf Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Miman You, Shuanhong Wang","submitted_at":"2014-10-30T07:28:26Z","abstract_excerpt":"Let $ Aut_{mHH}(H)$ denote the set of all automorphisms of a monoidal Hopf algebra $H$ with bijective antipode in the sense of Caenepeel and Goyvaerts \\cite{CG2011}. The main aim of this paper is to provide new examples of braided $T$-category in the sense of Turaev \\cite{T2008}. For this, first we construct a monoidal Hom-Hopf $T$-coalgebra $\\mathcal{MHD}(H)$ and prove that the $T$-category $Rep(\\mathcal{MHD}(H))$ of representation of $\\mathcal{MHD}(H)$ is isomorphic to $\\mathcal {MHYD}(H)$ as braided $T$-categories, if $H$ is finite-dimensional. Then we construct a new braided $T$-category $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8278","kind":"arxiv","version":3},"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"}