How Does Category Theory Enhance Understanding of Physics?

[klw1026@gmail.com]

I am currently working my way through classical Yang-Mills theory with
the help of John Baez's book on gauge fields and some others. I have
recently just began to notice the new, well new to myself, research on
higher gauge theory. This looks very interesting but I feel that my
background in category theory is too weak to actually understand
everything that is going on. This seems to be a recurring theme as I
try to advance my knowledge of mathematical physics. Last semester I
took a course on topological quantum field theory and another on
quantum groups and I feel that I did not get a lot out of it due to
the amount of category theory that was used. So my question is this:
does anyone know of a good reference for learning category theory? I
have looked at Mac Lane's book but find a bit "spooky" with the amount
of set theory he uses. Thanks for the help.

 

[Igor Khavkine]

On 2008-02-17, klw1026@gmail.com <klw1026@gmail.com> wrote:
> I am currently working my way through classical Yang-Mills theory with
> the help of John Baez's book on gauge fields and some others. I have
> recently just began to notice the new, well new to myself, research on
> higher gauge theory. This looks very interesting but I feel that my
> background in category theory is too weak to actually understand
> everything that is going on. This seems to be a recurring theme as I
> try to advance my knowledge of mathematical physics. Last semester I
> took a course on topological quantum field theory and another on
> quantum groups and I feel that I did not get a lot out of it due to
> the amount of category theory that was used. So my question is this:
> does anyone know of a good reference for learning category theory? I
> have looked at Mac Lane's book but find a bit "spooky" with the amount
> of set theory he uses. Thanks for the help.[/color]

John himself is fond of talking about category theory and its relation
to physics. So, not a bad place to start would be his own website. See
for instance [1] and [2]. The notes from his website are often presented
in a very casual manner, so to get the most out of them you might want
to followup on his references while working through them.

[1] http://math.ucr.edu/home/baez/categories.html
[2] http://math.ucr.edu/home/baez/QG.html

Hope this helps.

Igor

 

[Lou Pecora]

In article <slrnfrkkrd.fep.igor.kh@corum.multiverse.ca>,
Igor Khavkine <igor.kh@gmail.com> wrote:

> John himself is fond of talking about category theory and its relation
> to physics. So, not a bad place to start would be his own website. See
> for instance [1] and [2]. The notes from his website are often presented
> in a very casual manner, so to get the most out of them you might want
> to followup on his references while working through them.
>
> [1] http://math.ucr.edu/home/baez/categories.html
> [2] http://math.ucr.edu/home/baez/QG.html
>
> Hope this helps.
>
> Igor[/color]

I've just been lurking a little on this thread, but I looked at these
web pages and I would recommend them, too. Very nice intro to
Categories. And I started knowing nothing about categories. The
explanation of the lack of a functor from classical systems to quantum
systems that would represent a quantization was enlightening since it
also showed a good example of functors and categories and the
application.

--
-- Lou Pecora