# Post

Originally shared by John Baez

When chemists list a bunch of chemical reactions like

C + O₂ → CO₂

they are secretly describing a 'category'.

That shouldn't be surprising. A

f: x → y

The rules of a category say:

1) we can

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

3) every object x has an

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

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:

http://math.ucr.edu/home/baez/networks_oxford/networks_stochastic.pdf

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

**Chemists 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 writtenf: 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:

http://math.ucr.edu/home/baez/networks_oxford/networks_stochastic.pdf

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

Slides available here: http://math.ucr.edu/home/baez/networks_oxford/networks_stochastic.pdf Nature and the world of human technology are full of networks. P...

Shared with: Nicholas Guttenberg

*This post was originally on Google+*