Yes, thanks! I’ll fix this in the website version and the PDF file.

]]>Since, and , shouldn’t ?

]]>The same structure occurs in the more general setting of:

Lucas Dixon, Aleks Kissinger. Open Graphs and Monoidal Theories

which has been specifically developed for dealing with certain subtleties (e.g. scalars) when considering the diagrams in compact categories as graphs. (I am actually currently sitting in a talk about this.)

]]>Here is a related reference that John found and showed me a while back:

* Vladimiro Sassone (http://www.ecs.soton.ac.uk/people/vs), On the category of Petri net computations, 6th International Conference on Theory and Practice of Software Development, Proceedings of TAPSOFT ‘95_, Lecture Notes in Computer Science 915, Springer, Berlin, pp. 334-348. (http://eprints.ecs.soton.ac.uk/11951/1/strong-conf.pdf)

]]>Eugene wrote:

Is it correct to think that the category of bipartite graphs is a slice category Graph/C where Graph is the category of directed multigraphs and C is a graph with two vertices (square, rectangle) and two arrows? And this “is” your category of Petri nets?

That sounds correct—though again, I’ve paid no attention to the noninvertible morphisms in this category.

To get a differential equation I need a *stochastic* Petri net. But there’s a huge literature on plain Petri nets.

Also: I should warn you that there are probabily evil people lurking out there who treat ‘being bipartite’ as a *property* of a graph rather than a *structure*. For us it’s crucial to treat it as a structure.