Re: Fundamental Theorem of Category Theory?

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. Regards, Walter. Quoting Miles Gould <miles@assyrian.org.uk>:

On Fri, Jun 05, 2009 at 04:36:23PM -0400, Ellis D. Cooper wrote:

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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.

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