Re: Isomorphisms of categories

[jim stasheff <jds@math.upenn.edu>]

Peter May wrote:
> DeTeXing an exercise I routinely assign, here is
> an example of an isomorphism of categories that is
> not `accidental' in Peter Johnstone's sense and is
> always used in practice as an isomorphism and not
> merely an equivalence.
>
>
> The fundamental theorem of Galois theory:
>
> Let G = Gal(E/F) be the Galois group of a finite
> Galois extension E/F.  Define an isomorphism of
> categories between the category of intermediate
> fields F\subset K\subset E and field maps
> K >--> L that fix F pointwise and the category
> of orbits G/H and G-maps between them.
>
>
>
and an isomorphic category of coverings spaces such that...

jim



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