Since I was in Banff, my student Franciscus Rebro took over this week and explained more about cospan categories. These are a tool for constructing categories where the morphisms are networks such as electrical circuit diagrams, signal flow diagrams, Markov processes and the like. For some more details see:
• John Baez and Brendan Fong, A compositional framework for passive linear networks.
Cospan categories are really best thought of as bicategories, and Franciscus gets into this aspect too.