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:
To read more about the network theory project, go here: