Diagrammatic Polyhedral Algebra
Filippo Bonchi, Alessandro Di Giorgio, Pawel Sobocinski
TL;DR
An affine extension is axiomatised and soundness and completeness are proved for the prop of polyhedra and adding a register results in a concurrent extension of the calculus of signal flow graphs, powerful enough to capture continuous Petri nets.
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.