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Comment on Applied Category Theory at NIST (Part 2) by John Baez

Wed, 18 Apr 2018 23:20:39 +0000

That's a good idea. Actually Spencer Breiner should do it, since it's his workshop... but I'll be happy to get some of the fame and glory. (image)

Comment on Applied Category Theory at NIST (Part 2) by Keith Harbaugh

Wed, 18 Apr 2018 22:00:15 +0000

JB, thanks very, very much for posting this. What an intense experience those two days must have been! As the saying goes, "Like drinking water from a fire hose." And thanks to the organizers and participants. ---- Segueing to a slightly different topic, IMO a message to the Categories mailing list, with a link to http://www.appliedcategorytheory.org/nist-workshop-slides/ would be a very good idea. Would you be willing to post such a message? If for some reason you do not want to, I will see if Bob Rosebrugh would accept such a message from me, but it seems more appropriate for you to submit such a message. Thanks.

Comment on Applied Category Theory 2018 — Adjoint School by Applied Category Theory 2018 Schedule | Azimuth

Wed, 18 Apr 2018 19:07:48 +0000

Here’s the schedule for the ACT 2018 Adjoint School: (image)

Comment on Applied Category Theory at NIST (Part 1) by Applied Category Theory at NIST (Part 2) | Azimuth

Wed, 18 Apr 2018 05:47:42 +0000

Here are links to the slides and videos for most of the talks from "Applied Category Theory: Bridging Theory & Practice". They give a pretty good picture of what went on. Spencer Breiner put them up here; what follows is just a copy of what's on his site.

Comment on A Compositional Framework for Reaction Networks by Raphael

Tue, 17 Apr 2018 07:22:07 +0000

The Petri nets are familiar to the Chemist, though maybe not necessarily under that name :-). I see that you arrived at that by what we would call "reaction kinetic" considerations. When I started to think about it I had a different approach: just regard the thermodynamic equilibria. So the basic question is about the types of the products and not how long it takes to get them. That would be something like a "reaction mechanism network". (A side note here: what you write about the term "species" in Chemistry is entirely true, but there is another thing that can be mentioned, chemists are well trained to strictly separate between "particle/molecule,atom" and "compound" hierarchy. There is usually a set of terms which forms a partition with this respect and "species" strictly speaking belongs to the particle/molecule subset). So I thought about compounds (anything what you can put into any type of container) as the elements of the set $latex A=\{a,b,\dots\}$. And the binary operation (lets write it multiplicative for the moment) being a perfect mixture followed by infinite time. Then reactions read for example like $latex ab=cd$. Its clear that $latex aa=a$, you mix the compound with itself and nothing happens. (The nice feature of multiplicativity here I find is that total amounts do not appear, only concentrations.) Also $latex ab=ba$ is clear. But except closed-ness, there is nothing more. So my conclusion was its a CI-magma. What is missing are different reaction conditions at which we wait for the thermodynamic equilibrium. So I thought you get that by a set of indexed morphisms, the indices are the reaction conditions, I think its basically temperature and pressure, maybe some EM radiation. This morphism conserves idempotency and commutativity (besides closedness), so I thought one might call it "homomorphism" (but I am not sure). An interesting feature of this formalization is, that one can for example model that there is a difference between pouring $latex a$ into $latex b$ and $latex b$ into $latex a$, which seems to contradict commuativity at first glance, but thats not true: pouring a into b means essentially starting with $latex (((ab)b)b)b$ and going via $latex a((((ab)b)b)b)$ and $latex a(a((((ab)b)b)b))$ to $latex a(a(a((((ab)b)b)b)))$, which is $latex \ne b(b(b((((ba)a)a)a)))$ in a CI-magma. So in that approach "kinetics" would enter from an more algebraic side the buisnes. Would it make sense to you?

Comment on A Compositional Framework for Reaction Networks by Raphael

Tue, 17 Apr 2018 06:42:47 +0000

Interesting, thank you very much!

Comment on A Compositional Framework for Reaction Networks by John Baez

Mon, 16 Apr 2018 21:48:18 +0000

A common approach these days is to use a strict symmetric monoidal category where different substances (usually called 'species') are objects, the tensor product is denoted $latex +$ and a typical morphism would a reaction like this: $latex A + B \to C + D + D$ This is a tiny bit like a commutative idempotent magma, but different. You can read more in Section 25.2 here: • John Baez and Jacob Biamonte Quantum Techniques for Stochastic Mechanics, World Scientific Press, Singapore, 2018. (Draft available on the arXiv.)

Comment on A Compositional Framework for Reaction Networks by Raphael

Mon, 16 Apr 2018 20:56:01 +0000

I had myself some thoughts about the mathematics of chemical reactions. My bases was to note that the set of substances with the a binary operation is a "commutative idempotent magma" (CI-magmas), for obvious reasons. Reaction conditions are not included in this picture, so one way to introduce them would be some "homomorphism" taking care for that. I dunno if much results from that (the lit. on CI-magmas as far as I can see is sparse) but anyway I think this is at least a concise picture of the structure of the beast. Got some take on that?

Comment on Applied Category Theory 2018 by Applied Category Theory 2018 – Schedule | Azimuth

Fri, 13 Apr 2018 01:29:17 +0000

Here’s the schedule of the ACT2018 workshop: (image)

Comment on Diamonds and Triamonds by Diamonds | Complex Projective 4-Space

Mon, 09 Apr 2018 04:06:00 +0000

[…] John Baez elaborates on the sequence of ‘hyperdiamonds’, together with mentioning an alternative three-dimensional structure called the triamond, here. […]