Thanks for the replies. Pedantry or not aside, sounds like some interesting stuff is out there. I'm actually most hoping for a strait course on pure abstract categories, but it is always interesting to figure out what some of these guys are actually doing with it all.
My guess is that not much would be known, since the basic criterion of the fundamental theorem of finitely generated R-modules over a PID would not be met.
My way of saying I dunno. It sounds like an interesting question for which I am probably not equipped to help. Good luck.
I just have a quick, but odd question. Next term I will be taking a Category Theory class with a visiting professor from Moscow. The professor is known to have done most of his work in Physics. Does anyone have any experience using results from Category Theory applied to Physics?
Absolutely happens all the time. For example if anything can be described by a log function then it makes sense to look at the area under its curve, even as it approaches zero.
What you are describing is a singularity and physics (and indeed all of science) is rife with 'em.
Howdy, all. I am not sure if this is the right forum for this question. It isn't exactly an homework question, but it does stem very closely from a homework assignment in a first year graduate course in Abstract Algebra. The assignment has come and gone with limited success on my part, but...
From what I understand the Pythagoreans (the cult of number started by Pythagorus) held close the great secret of the irrationals. To them it was sacred but also frightening news about the imperfection of reality. So when one of them finally told someone and the secret was out that member of...