{"paper":{"title":"On the regular representation of an (essentially) finite 2-group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Josep Elgueta","submitted_at":"2009-07-06T12:46:13Z","abstract_excerpt":"The regular representation of an essentially finite 2-group $\\mathbb{G}$ in the 2-category $\\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is next shown that all hom-categories in $\\mathbf{Rep}_{\\mathbf{2Vect}_k}(\\mathbb{G})$ are 2-vector spaces under quite standard assumptions on the field $k$, and a formula giving the corresponding \"intertwining numbers\" is obtained which proves they are symmetric. Finally, it is shown that the forgetful 2-functor ${\\boldmath$\\omega$}:\\mathbf{Rep}_{\\mathbf{2Vect}_k}(\\mathbb{G})\\T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0978","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"}