{"paper":{"title":"On $3$-gauge transformations, $3$-curvature and $\\mathbf{Gray}$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CT","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Wei Wang","submitted_at":"2013-11-15T10:28:53Z","abstract_excerpt":"In the $3$-gauge theory, a $3$-connection is given by a $1$-form $A$ valued in the Lie algebra $ \\mathfrak g$, a $2$-form $B$ valued in the Lie algebra $\\mathfrak h $ and a $3$-form $C$ valued in the Lie algebra $ \\mathfrak l $, where $(\\mathfrak g,\\mathfrak h, \\mathfrak l)$ constitutes a differential $ 2$-crossed module. We give the $3$-gauge transformations from a $3$-connection to another, and show the transformation formulae of the $1$-curvature $2$-form, the $2$-curvature $3$-form and the $3$-curvature $4$-form. The gauge configurations can be interpreted as smooth $\\mathbf{Gray}$-functor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3796","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"}