The MIT Categories Seminar is an informal teaching seminar in category theory and its applications, with the occasional research talk. This spring they are meeting online each Thursday, 12 noon to 1pm Eastern Time.

The talks are broadcast over YouTube here, with simultaneous discussion on the Category Theory Community Server. (To join the channel, click here.) Talks are recorded and remain available on YouTube.

Here are some forthcoming talks:

March 26: David Jaz Myers (Johns Hopkins University) — Homotopy type theory for doing category theory.

April 2: Todd Trimble (Western Connecticut State University) — Geometry of regular relational calculus.

April 9: John Baez (UC Riverside) — Structured cospans and Petri nets.

April 16: Joachim Kock (Universitat Autònoma de Barcelona) — to be announced.

April 23: Joe Moeller (UC Riverside) — to be announced.

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Abstract. “Structured cospans” are a general way to study networks with inputs and outputs. Here we illustrate this using a type of network popular in theoretical computer science: Petri nets. An “open” Petri net is one with certain places designated as inputs and outputs. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Using the formalism of structured cospans, open Petri nets can be treated as morphisms of a symmetric monoidal category—or better, a symmetric monoidal double category. We explain two forms of semantics for open Petri nets using symmetric monoidal double functors out of this double category. The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. The second, a “reachability” semantics, simply says what these processes can accomplish. This is joint work with Kenny Courser and Jade Master.

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I’m giving a talk at the MIT Categories Seminar. It’ll be on Thursday April 9th, 12 noon Eastern Time.

You can already see the slides here.

The talk is based on these papers:

• John Baez and Kenny Courser, Structured cospans.

• John Baez and Jade Master, Open Petri nets.

• Jade Master, Generalized Petri nets.