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Gmane
From: Peter May <may <at> math.uchicago.edu>
Subject: Isomorphisms of categories
Newsgroups: gmane.science.mathematics.categories
Date: Saturday 29th May 2010 17:31:32 UTC (over 7 years ago)
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.



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CD: 2ms