# Categories of Nets

@article{Baez2021CategoriesON, title={Categories of Nets}, author={John C. Baez and Fabrizio Genovese and Jade Master and Michael Shulman}, journal={2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}, year={2021}, pages={1-13} }

We present a unified framework for Petri nets and various variants, such as pre-nets and Kock’s whole-grain Petri nets. Our framework is based on a less well-studied notion that we call Σ-nets, which allow fine-grained control over whether each transition behaves according to the collective or individual token philosophy. We describe three forms of execution semantics in which pre-nets generate strict monoidal categories, Σ-nets (including whole-grain Petri nets) generate symmetric strict…

## 9 Citations

A Categorical Semantics for Bounded Petri Nets

- Computer ScienceArXiv
- 2021

A categorical semantics for bounded Petri nets, both in the collective and individual-token philosophy, and proves, in both cases, that the internal and external constructions are equivalent, by using machinery built on top of the Grothendieck construction.

Whole-grain Petri nets and processes

- Computer Science
- 2020

A formalism for Petri nets based on polynomial-style conﬁgurations and etale maps that supports both a geometric semantics and an algebraic semantics in the style of Meseguer and Montanari, in terms of free coloured props.

A diagrammatic view of differential equations in physics

- Mathematics
- 2022

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put…

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

- Computer ScienceFrontiers in Systems Biology
- 2022

It is argued that without addressing the reproducibility crisis, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises the authors face.

Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages

- Mathematics, Computer ScienceProc. ACM Program. Lang.
- 2022

This paper gives a denotational semantics for the Pi family of reversible programming languages for boolean circuits, using weak groupoids à la Homotopy Type Theory, and shows how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of type isomorphisms.

Towards a Geometry and Analysis for Bayesian Mechanics

- Computer Science
- 2022

A simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms, providing a related, but alternative, formalism to those driven purely by descriptions of random dynamical systems, and taking a further step towards a comprehensive statement of the physics of self-organisation in formal mathematical language.

A Categorical Semantics for Hierarchical Petri Nets

- Computer ScienceGCM@STAF
- 2021

This paper shows how a particular flavor of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category to the category of sets and spans between them.

Dialectica Petri nets

- Computer ScienceArXiv
- 2021

This work revisits the use of the Dialectica construction as a categorical model for Petri nets generalizing the original application to suggest that Petrinets with different kinds of transitions can be modeled in the same categorical framework.

Sheaf representation of monoidal categories

- Mathematics
- 2020

. Every small monoidal category with universal ﬁnite joins of central idempotents is monoidally equivalent to the category of global sections of a sheaf of local monoidal categories on a topological…

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