#### John Baez

#### July 11, 2019

## Structured Cospans

Open systems of many kinds can be treated as morphisms in symmetric monoidal
categories. Two complementary approaches can be used to work with such
categories: props (which are more algebraic in flavor) and cospan categories
(which are more geometrical). In this talk we focus on the latter. Brendan
Fong's "decorated cospans" are a powerful tool for treating open systems
as cospans equipped with extra structure. Recently Kenny Courser has found
a simpler alternative, the theory of "structured cospans". We describe this
theory and sketch how it has been applied to a variety of open systems, such
as electrical circuits, Markov processes, chemical reactions and Petri nets.

You can see the slides here and
listen to a recording of my talk.

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

This talk is based on work with Kenny Courser and Christina Vasilakopoulou,
some of which appears in Courser's thesis:
To read more about the network theory project, go here:

© 2016 John Baez

baez@math.removethis.ucr.andthis.edu