Category Theory For Beginners: Open Dynamical Systems
Open dynamical systems can be composed in wiring diagrams as described by categorical systems theory. We introduce these well known ideas from categorical systems theory and the study of polynomial functors. We also discuss how bimorphic lenses can be used to describe wiring patterns of open dynamical systems.
We also propose that mode dependent open dynamical systems that can output other functions make good models of biological systems which can self replicate and rewire.
The ideas related to biology resulted from my collaboration with Jos Hoebe
https://www.researchgate.net/profile/...
Here are a few important references. Many more can be found by searching YouTube:
http://davidjaz.com/Papers/DynamicalB...
Polynomial Functors: A Mathematical Theory of Interaction
https://arxiv.org/abs/2312.00990
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