{"paper":{"title":"A Categorical Approach to L-Convexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.CT","authors_text":"Soichiro Fujii","submitted_at":"2019-04-17T05:40:56Z","abstract_excerpt":"We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\\overline{\\mathbb{Z}}$- or $\\overline{\\mathbb{R}}$-categories) and that of what we call ($\\overline{\\mathbb{Z}}$- or $\\overline{\\mathbb{R}}$-) extended L-convex sets. We introduce extended L-convex sets as variants of certain discrete structures called L-convex sets and L-convex polyhedra, studied in the field of discrete convex analysis. We also introduce homomorphisms between extended L-convex sets. The theorem claims that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08413","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"}