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 language | English |
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Pages (from-to) | 649-664 |
Number of pages | 16 |
Journal | Results in Mathematics |
Volume | 72 |
Issue number | 1-2 |
Early online date | 23 Mar 2017 |
DOIs | |
Publication status | Published - Sept 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