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DUALITY FOR CONVEX POLYTOPES

Part of: Categories and theories General convexity General theory of categories and functors Algebraic structures

Published online by Cambridge University Press:  01 June 2009

A. B. ROMANOWSKA ,
P. ŚLUSARSKI  and
J. D. H. SMITH
A. B. ROMANOWSKA*
Affiliation:
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland (email: [email protected])
P. ŚLUSARSKI
Affiliation:
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland (email: [email protected])
J. D. H. SMITH
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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This paper establishes a duality between the category of polytopes (finitely generated real convex sets considered as barycentric algebras) and a certain category of intersections of hypercubes, considered as barycentric algebras with additional constant operations.

Keywords

dualitymodesaffine spacesbarycentric algebrasconvex setssimplexhypercube

MSC classification

Secondary: 18C05: Equational categories 52A01: Axiomatic and generalized convexity 08A05: Structure theory 18A35: Categories admitting limits (complete categories), functors preserving limits, completions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 399 - 412
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This paper was written within the framework of INTAS project no. 03-51-4110.

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