[FOM] FOM Messing on isomorphism of categories (messing)
colin.mclarty at case.edu
Sat Jan 12 07:58:25 EST 2008
>From messing <messi001 at umn.edu>
Date Fri, 11 Jan 2008 09:06:48 -0600
accurately shows that many categorical (and 2-categorical, and other)
relations besides functor isomorphism are useful. Sans erreur.
Yet it remains that all work using categories *also* uses (1-
categorical) isomorphism of categories.
Messing offers SGA 4, Giraud's book Cohomologie non-abelienne, and
Laumon-Moret Bailly Champs algebrique as works which use relations
besides isomorphism between categories. Indeed they do.
But the chief device of SGA 4 is representable functors, and SGA 4
relies throughout on the fact that each one defines a representing
category uniquely up to isomorphism. This alone demonstrates that
isomophism of categories *has* serious mathematical uses. Personally I
already took Gelfand and Manin as serious.
I don't own either of the other books. But if my claim still seems
controversial and we can agree to let these two examples stand as
decisive test cases then I will undertake to get them and cite passages
where they use isomorphism of categories.
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