{"paper":{"title":"Conceptual Differential Calculus. I: First Order Local Linear Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CT","authors_text":"Wolfgang Bertram","submitted_at":"2015-03-16T12:31:06Z","abstract_excerpt":"We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or  infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina vector space or module,  a locally linear map  is defined to be a map respecting two canonical operationsliving \"over\" its domain of definition.These two operations are composition laws of a  canonical groupoid and of a  scaled action category, respectively,fitting together into a  canonical double category. Local linear algebra (of first order) is the stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04623","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"}