On Fri, Jun 05, 2009 at 04:36:23PM -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?
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. I've occasionally referred to this theorem as the Fundamental Theorem of Category Theory by way of emphasizing its importance while teaching, but I've always immediately clarified that it's only me who uses this term :-) Miles -- Sometimes it's best to do nothing, if it's the right sort of nothing. -- The Doctor [For admin and other information see: http://www.mta.ca/~cat-dist/ ]