• John C. Baez, David Weisbart and Adam Yassine, Open systems in classical mechanics.

The basic idea is by now familiar to fans of this blog—but there are some big twists! I like treating open systems as cospans with extra structure. But in this case it makes more sense to use *spans*, since the phase space of a classical system maps *to* the phase space of any subsystem. We’ll compose these spans using pullbacks.

Kenny’s talk explains the difference pretty well. Basically, decorated cospans that look isomorphic may not be technically isomorphic. There are just not enough isomorphisms between decorated cospans. As Kenny explains, structured cospans don’t suffer from this problem.

]]>• Jonathan Lorand and Fabrizio Genovese, Hypergraph categories of cospans, The *n*-Category Café, 28 February 2018.

Brendan was the first to join the project. I wanted him to work on electrical circuits, which are a nice familiar kind of network, a good starting point. But he went much deeper: he developed a general category-theoretic framework for studying networks. We then applied it to electrical circuits, and other things as well.

]]>Brendan was the first to join the project. I wanted him to work on electrical circuits, which are a nice familiar kind of network, a good starting point. But he went much deeper: he developed a general category-theoretic framework for studying networks. We then applied it to electrical circuits, and other things as well.

]]>I thought a normal vector field, where the points and the vectors are the decorated cospans (the arrows of the cospans like real vectors), so that graph and flow curves can coincides with a limit of close distance of the vector field representation.

If it is so, then many theorems of the decorated cospans can be applied to the vector fields (with some limits), and vice versa.

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