John Baez

Symposium on Compositional Structures 4

May 22, 2019

Props in Network Theory

To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. All these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. Two complementary approaches are presentations of props using generators and relations (which are more algebraic in flavor) and structured cospan categories (which are more geometrical). In this talk we focus on the former. A "prop" is a strict symmetric monoidal category whose objects are tensor powers of a single generating object. We will see that props are a flexible tool for describing many kinds of networks.

You can see the slides here.

This talk assumes considerable familiarity with category theory. For a much gentler talk on the same theme, see:

To read more about the network theory project, go here:


© 2019 John Baez
baez@math.removethis.ucr.andthis.edu

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