{"paper":{"title":"Normed modules and the categorification of integrations, series expansions, and differentiations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.FA"],"primary_cat":"math.RT","authors_text":"Panyue Zhou, Shengda Liu, Yu-Zhe Liu, Zhaoyong Huang","submitted_at":"2024-05-05T00:19:37Z","abstract_excerpt":"We explore the assignment of norms to $\\mathit{\\Lambda}$-modules over a finite-dimensional algebra $\\mathit{\\Lambda}$, resulting in the establishment of normed $\\mathit{\\Lambda}$-modules. Our primary contribution lies in constructing two new categories $\\mathscr{N}\\!\\!or^p$ and $\\mathscr{A}^p$, where each object in $\\mathscr{N}\\!\\!or^p$ is a normed $\\mathit{\\Lambda}$-module $N$ limited by a special element $v_N\\in N$ and a special $\\mathit{\\Lambda}$-homomorphism $\\delta_N: N^{\\oplus 2^{\\dim\\mathit{\\Lambda}}} \\to N$, the morphism in $\\mathscr{N}\\!\\!or^p$ is a $\\mathit{\\Lambda}$-homomorphism $\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02777","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/2405.02777/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"}