Petri nets

Numerous authors have proposed category-theoretic interpretations of Petri nets. The original seems to be:

• Meseguer & Montanari, 1990: Petri nets are monoids (doi, pdf)

By John Baez and collaborators, as part of the network theory program:

• Baez & Pollard, 2017: A compositional framework for reaction networks (doi, arxiv, nCat Cafe , Azimuth )
• Baez & Master, 2018: Open Petri nets (arxiv, Azimuth 1 ,2 )
• Master, 2019: Generalized Petri nets (arxiv)
• Baez, Foley, Moeller, 2019: Network models from Petri nets with catalysts (arxiv, nCat Cafe , Azimuth )
• Baez, Genovese, Master, Shulman, 2021: Categories of nets (arxiv, nCat Cafe 1 ,2 , Azimuth 1 ,2 )

By Fabrizio Genovese and collaborators, some of which for Statebox :

• Genovese & Herold, 2018: Executions in (semi-)integer Petri nets are compact closed categories (arxiv)
• Genovese et al, 2019: Computational Petri nets: Adjunctions considered harmful (arxiv)
• Genovese, Herold, and the Statebox team, 2019: The mathematical specification of the Statebox language (arxiv)
• Genovese, 2019: The essence of Petri net gluings (arxiv)
• Genovese & Spivak, 2020: A categorical semantics for guarded Petri nets (doi, arxiv)
• Genovese, Loregian, Palombi, 2021: Nets with mana: A framework for chemical reaction modelling (arxiv)
• Genovese, Loregian, Palombi, 2021: A categorical semantics for bounded Petri nets (arxiv)
• Genovese & Herold, 2021: A categorical semantics for hierarchical Petri nets (arxiv)

Further works on Petri nets:

• Kock, 2022: Whole-grain Petri nets and processes (arxiv)
  • Introduces whole-grain Petri nets, a variant of Petri net defined as presheaves
  • First version at ACT 2020 was called “Elements of Petri nets and processes”