Year: 2015
Type: preprint
Abstract: We apply a categorical lens to the study of betweenness relations by capturing them within a topological category, fibred in lattices, and study several subcategories of it. In particular, we show that its full subcategory of finite objects forms a Fraissé class implying the existence of a countable homogenous betweenness relation. We furthermore show that the subcategory of antisymmetric betweenness relations is reflective. As an application we recover the reflectivity of distributive complete lattices within complete lattices, and we end with some observations on the Dedekind-MacNeille completion.
Source: arXiv (Cornell University)
Authors: Bruno, J., McCluskey, A., Szeptycki, P.
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952444381