Dear Ellis, On Fri, 5 June 2009 16:36:23 -0400, Ellis D. Cooper wrote: | There are Fundamental Theorems of Arithmetic, Algebra, Calculus, and | indeed, many more. | My question is, What would be candidates for the Fundamental Theorem | of Category Theory? | Yoneda Lemma comes to my mind. What do you think? I have asked Prof. Yoneda many years ago why Yoneda Lemma is called "Lemma", not "Theorem". He said that perhaps it was a bit about internal of category theory rather than insisting on applications to other mathematics. Doesn't Yoneda Lemma satisfy (c) in Mile Gould's post? I don't know how much Yoneda Lemma is useful in other areas of mathematics, and I have wanted to know it. On Sat, 6 June 2009 23:22:52 +0100, Miles Gould wrote: | My suggestion would be the theorem that left adjoints preserve colimits, | and right adjoints preserve limits. | This may not be the deepest theorem in category theory, but | (a) it's pretty darn deep, | (b) it describes a beautiful connection between two fundamental notions | in the subject, | (c) it admits a huge variety of applications in "ordinary" mathematics. Best Regards, Makoto Hamana [For admin and other information see: http://www.mta.ca/~cat-dist/ ]