John C. Baez's Blog, page 55

Noether’s Theorem

 

I’ve been spending the last month at the Centre of Quantum Technologies, getting lots of work done. This Friday I’m giving a talk, and you can see the slides now:

• John Baez, Getting to the bottom of Noether’s theorem.

Abstract. In her paper of 1918, Noether’s theorem relating symmetries and conserved quantities was formulated in term of Lagrangian mechanics. But if we want to make the essence of this relation seem as self-evident as possible, we can turn to a formulation in term of Po...

Compositionality – Now Open For Submissions

Our new journal Compositionality is now open for submissions!

It’s an open-access journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline. Topics may concern foundational structures, an organizing principle, or a powerful tool. Example areas include but are not limited to: computation, logic, physics, chemistry, engineering, linguistics, and cognition.

Compositionality is free of cost for both readers and authors.

CALL FOR PAPERS

We in...

Complex Adaptive System Design (Part 8)

John Foley, Joe Moeller and I have made some nice progress on compositional tasking for the Complex Adaptive System Composition and Design Environment project.

‘Compositional tasking’ means assigning tasks to networks agents in such a way that you can connect or even overlay such tasked networks and get larger ones. This lets you build up complex plans from smaller pieces.

In my last post in this series, I sketched an approach using ‘commitment networks’. A commitment network is a graph where...

Open Petri Nets (Part 3)

I’ve been talking about my new paper with Jade Master:

• John Baez and Jade Master, Open Petri nets.

In Part 1 we saw the double category of open Petri nets; in Part 2 we saw the reachability semantics for open Petri nets as a double functor. Now I’d like to wrap up by showing you the engine beneath the hood of our results.

I fell in love with Petri nets when I realized that they were really just presentations of free symmetric monoidal categories. If you like category theory, this turns Petr...

Open Petri Nets (Part 2)

I’d like to continue talking about this paper:

• John Baez and Jade Master, Open Petri nets.

Last time I explained, in a sketchy way, the double category of open Petri nets. This time I’d like to describe a ‘semantics’ for open Petri nets.

In his famous thesis Functorial Semantics of Algebraic Theories, Lawvere introduced the idea that semantics, as a map from expressions to their meanings, should be a functor between categories. This has been generalized in many directions, and the same idea...

Open Petri Nets (Part 1)

Jade Master and I have just finished a paper on open Petri nets:

• John Baez and Jade Master, Open Petri nets.

Abstract. The reachability semantics for Petri nets can be studied using open Petri nets. For us an ‘open’ Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category, which becomes symmetric monoidal under di...

Open Petri Nets

Jade Master and I have nearly finished a paper on open Petri nets, and it should appear on the arXiv soon. I’m excited about this, especially because our friends at Statebox are planning to use open Petri nets in their software. They’ve recently come out with a paper too:

• Fabrizio Romano Genovese and Jelle Herold, Executions in (semi-)integer Petri nets are compact closed categories.

Petri nets are widely used to model open systems in subjects ranging from computer science to chemistry. The...

The Philosophy and Physics of Noether’s Theorems

 

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I’ll be speaking at a conference celebrating the centenary of Emmy Noether’s work connecting symmetries and conservation laws:

• The Philosophy and Physics of Noether’s Theorems, 5-6 October 2018, Fischer Hall, 1-4 Suffolk Street, London, UK. Organized by Bryan W. Roberts (LSE) and Nicholas Teh (Notre Dame).

They write:

2018 brings with it the centenary of a major milestone in mathematical physics: the publication of Amalie (“Emmy”) Noether’s theorems relating symmetry and physical quanti...

Compositionality: the Editorial Board

The editors of this journal have an announcement:

We are happy to announce the founding editorial board of Compositionality, featuring established researchers working across logic, computer science, physics, linguistics, coalgebra, and pure category theory (see the full list below). Our steering board considered many strong applications to our initial open call for editors, and it was not easy narrowing down to the final list, but we think that the quality of this editorial board and the gen...

Applied Category Theory Course: Collaborative Design

In my online course we’re reading the fourth chapter of Fong and Spivak’s book Seven Sketches. Chapter 4 is about collaborative design: building big projects from smaller parts. This is based on work by Andrea Censi:

• Andrea Censi, A mathematical theory of co-design.

The main mathematical content of this chapter is the theory of enriched profunctors. We’ll mainly talk about enriched profunctors between categories enriched in monoidal preorders. The picture above shows what one of these...