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Tim HuttonTim Hutton - 2014-03-17 01:54:45+0000 - Updated: 2014-03-17 01:54:45+0000
Originally shared by John BaezChemists are secretly doing applied category theory

When chemists list a bunch of chemical reactions like

C + O₂ → CO₂

they are secretly describing a 'category'.

That shouldn't be surprising.  A category is simply a collection of things called objects together with things called arrows going from one object to another, often written

f:  x → y

The rules of a category say:

1) we can compose an arrow f:  x → y and another arrow g: y → z to get an arrow gf: x → z,

2) (hg)f = h(gf) so we don't need to bother with parentheses when composing arrows,

3) every object x has an identity object 1ₓ: x → x that obeys 1ₓ f = f and f 1ₓ = f.

Whenever we have a bunch of things (objects) and processes (arrows) that take one thing to another, we're likely to have a category. 

In chemistry, the objects are bunches of molecules and the arrows are chemical reactions.  But we can 'add' bunches of molecules and also add reactions, so we have something more than a mere category: we have something called a symmetric monoidal category

My talk here is an explanation of this viewpoint and how we can use it to take ideas from elementary particle physics and apply them to chemistry!   You can see the slides here:

Click on anything in blue, or any picture, and you'll get more information.

Slides available here: Nature and the world of human technology are full of networks. P...

Shared with: Nicholas Guttenberg

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