Diagrammatic Polyhedral Algebra
Filippo Bonchi, Alessandro Di Giorgio, Pawel Sobocinski
TL;DR
This paper develops a diagrammatic algebraic framework for polyhedral cones and polyhedra, providing sound and complete axiomatizations for their corresponding algebraic structures.
Contribution
It extends Interacting Hopf algebras with an order primitive and introduces axiomatizations for polyhedral cones and polyhedra.
Findings
Sound and complete axiomatization of the prop of polyhedral cones.
Axiomatization of an affine extension for polyhedra.
Proofs of soundness and completeness for these algebraic structures.
Abstract
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of polyhedra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics