Network theory

Network theory , not to be confused with network science, is a research program by John Baez and collaborators on the mathematical modeling of networks (processes) in science and engineering.

Literature

Electrical engineering and control theory

  • Baez & Fong, 2015: A compositional framework for passive linear networks (arxiv, nCat Cafe , Azimuth )
    • Fong, 2016, PhD thesis: The algebra of open and interconnected systems (arxiv)
  • Baez & Erbele, 2015: Categories in control (arxiv, pdf, nCat Cafe , Azimuth )
    • Erbele, 2016, PhD thesis: Categories in control: applied PROPs (arxiv)
    • Sec. 6: Closely related independent work:
      • Bonchi, Sobocinski, Zanasi, 2014: A categorical semantics of signal flow graphs (doi, pdf)
      • Bonchi, Sobocinski, Zanasi, 2015: Full abstraction for signal flow graphs (doi)
      • Bonchi, Sobocinski, Zanasi, 2017: Interacting Hopf algebras (doi, arxiv)
      • Wadsley & Woods, 2015: PROPs for linear systems (arxiv, nCat Cafe )
  • Baez, Coya, Rebro, 2017: Props in network theory (arxiv, nCat Cafe , talk )
    • Coya, 2018, PhD thesis: Circuits, bond graphs, and signal-flow diagrams: A categorical perspective (arxiv, nCat Cafe )

Markov processes and Petri nets

See the dedicated pages on Markov processes and Petri nets.

Network models

  • Baez, Foley, Moeller, Pollard, 2020: Network models (pdf, arxiv, Azimuth )
    • Moeller, 2020: Noncommutative network models (doi, arxiv)
    • Baez & Foley, 2021, in AMS Notices: Operads for designing systems of systems (pdf)
    • Network models have connections to Petri nets
  • Moeller & Vasilakopoulou, 2020: Monoidal Grothendieck construction (pdf, arxiv, Azimuth 1 ,2 , nLab )
    • Sec. 5: Examples inspired by network theory
    • Moeller, 2021, PhD thesis: The Grothendieck construction in categorical network theory (arxiv)

Decorated and structured cospans

  • Fong, 2015: Decorated cospans (pdf, arxiv, nCat Cafe )
  • Baez & Courser, 2019: Structured cospans(pdf, arxiv, nCat Cafe , Azimuth )
    • Courser, 2019, PhD thesis: Open systems: a double categorical perspective (arxiv, nCat Cafe 1 ,2 , Azimuth 1 ,2 )
    • Baez, Courser, Vasilakopoulou, 2021: Structured versus decorated cospans (arxiv, nCat Cafe 1 ,2 , Azimuth 1 ,2 )
  • Cicala, 2020: Rewriting structured cospans (arxiv)
    • Cicala, 2019, PhD thesis: Rewriting structured cospans: a syntax for open systems (arxiv)
    • Cicala & Courser, 2018: Spans of cospans in a topos (pdf)
    • Cicala, 2018: Spans of cospans (pdf)

Miscellaneous

  • Baez, Weisbart, Yassine, 2017: Open systems in classical mechanics (arxiv)
    • Weisbart & Yassine, 2020: Constructing span categories from categories without pullbacks (arxiv)