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Stream: deprecated: our papers

Topic: Categories of Nets

John Baez (Jan 17 2021 at 23:19):

A Petri net looks like a very simple thing:

But it turns out to conceal some subtleties... and in fact people have been struggling with these for at least 30 years, ever since Montanari and Meseguer wrote their paper 'Petri nets as monoids'.

Fabrizio Genovese, Jade Master, Mike Shulman and I have a new paper that clarifies what's going on. You can see this blog article for a quick explanation:

Categories of nets.

We describe 3 kinds of net, each of which naturally generates its own kind of monoidal category:

pre-nets, which generate free strict monoidal categories.
$\Sigma$ -nets, which generate free symmetric strict monoidal categories.
Petri nets, which generate free commutative monoidal categories.

and we show how they're all related!

Eric Forgy (Jan 17 2021 at 23:21):

Talk about a dream team! :muscle: Can't wait to read it :books:

Mike Shulman (Jan 19 2021 at 19:44):

Part 2 of the blog post

John Baez (Jan 19 2021 at 21:53):

Wow, you explained all the most important things I left out, without getting into anything technical!

John Baez (Jan 19 2021 at 21:53):

(The technical stuff is great too, but not for a blog article.)

Fabrizio Genovese (Apr 01 2021 at 13:51):

The paper Categories of nets by @John Baez , me, @Jade Master and @Mike Shulman got accepted to LiCS. It's about Petri nets that do amazing stuff, here's also a tweet about it!