[FOM] FOM Messing on isomorphism of categories (messing)

Colin McLarty 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.

best, Colin  

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