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I have created a stub for this at Petri net. I hope to develop the links with higher dimensional automata and also with linear logic.
I do not see Petri net. Is the capitalization correct ?
It was at Petri nets (plural). I’ve changed the name to Petri net.
OOPS! Sorry and thanks. The plural form was used in a list and I forgot to change it properly.
Any help on the link with LL would be appreciated. I know the systems modelling aspect which I have taught (and thoroughly enjoyed that as did the students as it seems to be an abstraction that somehow made sense to them.) I know the LL part but less well. Here I am following an agenda to explore the recent preprint by Goubault and Mimram on cubical sets, higher transitions systems etc. so initially I will try to write those parts that are needed for that aim, but feel that it is good stuff and some of the other aspects need exploring as well.
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It ends
In fact, the relationships between the various notions of net in our work have analogues in topology. On one hand, a manifold can always be given “local coordinates”, but it is too restrictive to ask that such coordinates be preserved strictly by maps between manifolds. Such coordinates can be regarded as analogous to the orderings on sources and targets in a pre-net. On the other hand, when a group acts on a manifold, the quotient topological space may no longer be a manifold,but has singularities at points of non-free action. This “coarse moduli space” can be regarded as analogous to a Petri net, where symmetry information has been lost. Kock’s whole-grain Petri nets are analogous to abstract manifolds themselves:they are free of undesirable “coordinates”, but neither can they have singularities. Finally, our Σ-nets play the role of orbifolds, coordinate-free manifold-like structures that retain the information of “isotropy groups” at singular points, yielding a better-behaved notion of quotient.
I mentioned to John that Proper orbifold cohomology might be worth comparing.
It looks to me like this analogy is not very specific to the notion of orbifolds, rather it seems to allude to the general situation of forming quotients of objects presented by generators and relations.
Yeah, there’s nothing topological or smooth about it.
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