On Mon, Jun 08, 2009 at 07:44:40AM -0400, tholen@mathstat.yorku.ca wrote:
You could make your choice more comprehensive: Freyd's General and Special Adjoint Functor Theorems give a more complete picture of the fundamental relationship between limit preservation and adjointness.
Indeed. I think there's an analogy to be made between these theorems and the Fundamental Theorem of Calculus: one side is very simply stated, and the other requires more care. Compare * d/dx (integral f(x) dx) = f(x), * integral (d/dx f(x)) dx = f(x) [up to constant offset...] with * all right adjoints preserve limits, * all limit-preserving functors [satisfying some caveats...] are right adjoints. Miles [For admin and other information see: http://www.mta.ca/~cat-dist/ ]