John Baez

Category Theory 2019

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:

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© 2016 John Baez