Decorated cospans are a framework for studying open systems invented by Brendan Fong. Since I’m now visiting the institute he and David Spivak set up—the Topos Institute—it was a great time to give a talk explaining the history of decorated cospans, their problems, and how those problems have been solved:
Structured vs Decorated Cospans
Abstract. One goal of applied category theory is to understand open systems: that is, systems that can interact with the external world. We compare two approaches to describing open systems as morphisms: structured and decorated cospans. Each approach provides a symmetric monoidal double category. Structured cospans are easier, decorated cospans are more general, but under certain conditions the two approaches are equivalent. We take this opportunity to explain some tricky issues that have only recently been resolved.
It’s probably best to get the slides here and look at them while watching this video:
If you prefer a more elementary talk explaining what structured and decorated cospans are good for, try these slides.
For videos and slides of two related talks go here:
For more, read these:
• Brendan Fong, Decorated cospans.
• Evan Patterson and Micah Halter, Compositional epidemiological modeling using structured cospans.
• John Baez and Kenny Courser, Structured cospans.
• John Baez, Kenny Courser and Christina Vasilakopoluou, Structured versus decorated cospans.
• Kenny Courser, Open Systems: a Double Categorical Perspective.
• Michael Shulman, Framed bicategories and monoidal fibrations.
• Joe Moeller and Christina Vasilakopolou, Monoidal Grothendieck construction.
To read more about the network theory project, go here: