Re: Fundamental Theorem of Category Theory?

[Miles Gould <miles@assyrian.org.uk>]

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


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