John Baez

Yorkshire and Midlands Category Seminar, February 5, 2021

The Berkeley Seminar, Topos Institute, July 28, 2021

Structured vs Decorated Cospans

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.

For my talk at the Yorkshire and Midlands Category Seminar explaining some applications, go here.

For my talk at the Topos Institute explaining some problems and how they were finally overcome, go here for the slides, and watch this video here:

For videos and slides of two related talks go here:

• Structured cospans and double categories.
• Structured cospans and Petri nets.

• 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:

• Network Theory.

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