To describe systems composed of interacting parts, scientists and
engineers draw diagrams of networks: flow charts, Petri nets,
electrical circuit diagrams, signal-flow graphs, chemical reaction
networks, Feynman diagrams and the like. In principle all these
different diagrams fit into a common framework: the mathematics of
symmetric monoidal categories. This has been known for some
time. However, the details are more challenging, and ultimately more
rewarding, than this basic insight. Two complementary approaches are
presentations of symmetric monoidal categories using generators and
relations (which are more algebraic in flavor) and decorated cospan
categories (which are more geometrical). In this talk we focus on the
latter.