A Compositional Framework for Reaction Networks

• One can easily turn a [[Petri net#Reaction network \((S, T, s, t)\) | reaction network]] into a Petri net and vice versa.
• category: \(RxNet\)
  • morphism: open Petri net goes from X to Y
  • symmetric monoidal category
• category: \(Dynam\)
  • : a category of open dynamical systems
  • morphism: open dynamical system
  • symmetric monoidal category
• category: \(SemiAlgRel\)
  • semi-algebraic relations between real vector spaces
  • relations defined by polynomials and inequalities
• functor: \(Gb: RxNet \rightarrow Dynam\)
  • greybox: hides some but not all internal details of an open Petri net
• functor: \(Bb: Dynam \rightarrow SemiAlgRel\)
  • blackbox:

Decorated cospans

• : a powerful general tool for describing open systems

graph TD
   S
   X -->|i| S
   Y -->|o| S

• in FinSet, the category of finite sets and functions
  • apex of the cospan is the set of states of an open system
  • legs of the cospan describe how inputs and outputs are included in the system