Reference List: Categorical Network Theory

By “categorical network theory”, I mean the study of networks or graphs using category theory. A lot of the time, the graphs in these works are morphisms in a category, or 1-cells in some sort of 2-dimensional category.

Here are some papers on categorical network theory:

1. 2013 Spivak, The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
2. 2013 Rupel, Spivak, The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes
3. 2015 Baez, Erbele, Categories in control
4. 2015 Lerman, Spivak, Vagner, Algebras of open dynamical systems on the operad of wiring diagrams
5. 2016 Baez, Fong, A compsitional framework for passive linear networks
6. 2016 Pollard, Open Markov processes: a compositional perspective on non-equilibrium steady states in biology
7. 2016 Baez, Fong, Pollard, A compositional framework for Markov processes
8. 2016 Coya, Fong, Corelations are the prop for extraspecial commutative Frobenius monoids
9. 2017 Baez, Pollard, A compositional framework for reaction networks
10. 2017 Lerman, Spivak, An algebra of open continuous time dynamical systems and networks
11. 2017 Coya, A compositional framework for bond graphs
12. 2017 Schultz, Spivak, Temporal type theory: a topos-theoretic approach to systems and behavior
13. 2017 Cicala, Spans of cospans
14. 2017 Pollard, Open Markov processes and reaction networks
15. 2018 Baez, Coya, Rebro, Props in network theory
16. 2018 Lerman, Networks of open systems
17. 2018 Baez, Foley, Moeller, Pollard, Network models
18. 2018 Cicala, Courser, Spans of cospans in a topos
19. 2018 Cicala, Categorifying the ZX-calculus
20. 2018 Baez, Courser, Coarse-graining open Markov processes