Betweenness Relations in a Categorical Setting

J. Bruno, A. McCluskey, P. Szeptycki

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)649-664
Number of pages16
JournalResults in Mathematics
Volume72
Issue number1-2
Early online date23 Mar 2017
DOIs
Publication statusPublished - Sep 2017

Keywords

  • antisymmetry
  • Betweenness relations
  • distributive closure
  • Grothendieck firbration
  • lattices
  • MacNeille completion
  • partial order
  • preorder
  • R-relations
  • road systems
  • separativity

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

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