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Category Theory and Physics

  1. Feb 17, 2008 #1
    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.
     
  2. jcsd
  3. Feb 19, 2008 #2
    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.


    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
     
  4. Feb 20, 2008 #3
    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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