#### John Baez

#### May 4, 2018

## Props in Network Theory

The challenge of global warming brings into clear view the need
for improved integration between category theory and other fields.
Among other things, we need categories to understand *networks*.
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 decorated cospan
categories (which are more geometrical). In this talk we focus on the
former.

You can see the slides here
and watch a video here.

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

For the other approach to network theory, decorated cospans, try this talk:
To read more about the network theory project, go here:

© 2016 John Baez

baez@math.removethis.ucr.andthis.edu