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Category Theory and Physics 
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#1
Feb1708, 05:00 AM

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I am currently working my way through classical YangMills 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. 


#2
Feb1908, 05:00 AM

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On 20080217, klw1026@gmail.com <klw1026@gmail.com> wrote:
> I am currently working my way through classical YangMills 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. 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 


#3
Feb2008, 05:00 AM

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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 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 


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