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Since I'm at the University of Wisconsin, busy talking to Gheorge Craciun and David Anderson about chemical reaction networks, there will be no class today! Instead, if you're curious, you can look at the slides of the talk I gave yesterday:
Abstract. Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.
This is about some aspects of category theory that I hope we'll get into later in the course! But it's supposed to be easy to understand, since it was for a general audience of mathematicians who don't even know the definition of a category.
It's a bit harder to understand without me talking, I'm afraid. For more explanations try these papers! For category theory applied to networks:
Brendan Fong, The Algebra of Open and Interconnected Systems
John Baez and Brendan Fong, A compositional framework for passive linear networks.
For more on Petri nets and reaction networks: