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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeNov 16th 2010

    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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 16th 2010

    I do not see Petri net. Is the capitalization correct ?

    • CommentRowNumber3.
    • CommentAuthorFinnLawler
    • CommentTimeNov 16th 2010

    It was at Petri nets (plural). I’ve changed the name to Petri net.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeNov 16th 2010

    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.

    • CommentRowNumber5.
    • CommentAuthorJoe Moeller
    • CommentTimeOct 5th 2019

    Added a reference connecting Petri nets and linear logic by Engberg and Winskel.

    diff, v10, current

    • CommentRowNumber6.
    • CommentAuthorJoe Moeller
    • CommentTimeOct 5th 2019

    added references to Petri nets are monoids by Meseguer and Montanari, and Quantum Techniques in stochastic mechanics by Baez and Biamonte

    diff, v11, current

  1. Added (and moved) references to categorical semantics

    Jade Master

    diff, v12, current

  2. Added section on categorical semantics

    Jade Master

    diff, v12, current

  3. Corrected typos and added to categorical semantics section

    Jade Master

    diff, v12, current

  4. Made the example of behavior in a commutative monoidal category more convincing.

    Jade Master

    diff, v13, current

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 18th 2021
    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 18th 2021

    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.

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2021

    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.

    • CommentRowNumber14.
    • CommentAuthorMike Shulman
    • CommentTimeJan 18th 2021

    Yeah, there’s nothing topological or smooth about it.

  5. added anchor tag

    Jade Master

    diff, v16, current

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