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Betweenness relations in a categorical setting

Bruno, J.
; 
McCluskey, A.
; 
Szeptycki, P.
Identifiers
http://hdl.handle.net/10379/10568
 https://doi.org/10.13025/28273
Publication Date
2017-03-23
Keywords
betweenness relations, r-relations, road systems, antisymmetry, separativity, distributive closure, grothendieck firbration, macneille completion, lattices, preorder, partial order, lattices
Type
Article
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Citation
Bruno, J. McCluskey, A.; Szeptycki, P. (2017). Betweenness relations in a categorical setting. Results in Mathematics 72 (1), 649-664
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 Fraiss, 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.
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Publisher
Springer Nature
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)