A Categorical Approach to L-Convexity

Abstract

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 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.

67 pages, Bachelor's thesis

References in corpus (1)

• Tight spans, Isbell completions and semi-tropical modules