#### John Baez

#### 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