{"paper":{"title":"An Ultrametric for Cartesian Differential Categories for Taylor Series Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Jean-Simon Pacaud Lemay","submitted_at":"2024-05-29T19:48:48Z","abstract_excerpt":"Cartesian differential categories provide a categorical framework for multivariable differential calculus and also the categorical semantics of the differential $\\lambda$-calculus. Taylor series expansion is an important concept for both differential calculus and the differential $\\lambda$-calculus. In differential calculus, a function is equal to its Taylor series if its sequence of Taylor polynomials converges to the function in the analytic sense. On the other hand, for the differential $\\lambda$-calculus, one works in a setting with an appropriate notion of algebraic infinite sums to forma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}