A Compositional Framework for Reaction Networks

• One can easily turn a 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

• 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