Structured Cospans

John Baez (UC Riverside)

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.