Tutorial: Categories for the practicing physicist

Tutorial: Categories for the practicing physicist

[Bob Coecke]

We have put a tutorial on symmetric monoidal categories on the arXiv:

http://arxiv.org/abs/0905.3010
Categories for the practising physicist (104 pages)
Bob Coecke and Eric Oliver Paquette

It is directed to physicists who unlike mathematical physicists, do not
have a strong background in pure maths.  The target audience are
researchers in quantum foundations and quantum infomation.  The main goal
is to show that monoidal categories are a natural starting point to craft
theories of physics, and that they are closely related to something
physicists are very used to, namely Dirac notation.  Some effort is made
to unpack the definition of a symmetric monoidal category which given its
`size', is just too much to grasp at once.  On the other hand, there is a
very clear physical intuition to monoidal categories which can be easily
grasped by physicists or any other operational scientist.  This tutorial
starts from this operational intuition and gradually converts it on
mathematical substance.  As a consequence, the attempt to convey a story
is more prominent than mathematical rigor.  In our interaction with
quantum foundationalists and quantum informaticians we noticed a great
need for a tutorial of this nature.



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