2019/04/17 by Soichiro Fujii, Fujii, Soichiro · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Rough Sets and Fuzzy Logic #math.CT #math.MG #math.OC
paper · pdf · doi:10.48550/arxiv.1904.08413
67 pages, Bachelor's thesis
arxiv created 2019/04/17 · openalex publication_date 2019/04/17 · arxiv updated 2019/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℤ- or ℝ-categories) and that of what we call (ℤ- or 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 there is a one to one correspondence (up to isomorphism) between two classes. The thesis also contains an introductory chapter on enriched categories and no categorical knowledge is assumed.