nLab category theory for dynamical systems

Idea

On category theory (and higher category theory) for the conceptualization and description of dynamical systems.

Related concepts

• lens (in computer science)

• para construction

• double category

• doubly indexed category

• polynomial functors

References

• Patrick Schultz, David I. Spivak, Christina Vasilakopoulou, Dynamical Systems and Sheaves, Appl Categor Struct 28 (2020) 1–57 [arXiv:1609.08086, doi:10.1007/s10485-019-09565-x]

• David Jaz Myers, Double Categories of Open Dynamical Systems, EPTCS 333 (2021) 154-167 [arXiv:2005.05956, doi:10.4204/EPTCS.333.11]

• Matteo Capucci, Bruno Gavranović, Jules Hedges, Eigil F. Rischel, Towards Foundations of Categorical Cybernetics, EPTCS 372 (2022) 235-248 [arXiv:2105.06332, doi:10.4204/EPTCS.372.17]

Monographs:

• David Spivak, Nelson Niu, Polynomial Functors: A General Theory of Interaction [webpage, pdf]

  (via polynomial functors)

• David Jaz Myers, Categorical systems theory, book project [github, pdf]

  (via virtual double categories)

Exposition:

• David Jaz Myers, Categorical systems theory, Topos Institute Blog (Nov 2021)

• David Jaz Myers, Double Categories of Dynamical Systems (2020) [pdf]

On a triple category-generalization of the para construction for systems theory:

• David Jaz Myers, The Para construction as a distributive law, talk at the Virtual Double Categories Workshop (2022) [slides, video]

• Matteo Capucci, Constructing triple categories of cybernetic processes [slides, video]

• Matteo Capucci, Para Construction as a Wreath Product, talk at CQTS (Jan 2024) [slides: pdf]