Re: Fundamental Theorem of Category Theory?

["Fred E.J. Linton" <fejlinton@usa.net>]

Once, long, long ago, I looked up the Yoneda paper 
then cited as source for the Y.L. 
Agreed: not there. 

But, in another Yoneda paper ("On Ext and exact sequences",
perhaps, I'm relying on memory alone, here), it *is* there,
not called Y.L., of course, but describing, as I recall, 
the connection between n.t.(hom(A, -), hom(B, -)) and 
hom(B, A) in the case that the hom-sets are the 
Ext equivalence classes (the only case of interest 
for that paper).

It didn't take much, either, to see the underlying 
Y.L. structure in the main proof there.

Cheers (and more detail, if called for,
once I'm back from Montrreal), 

-- Fred

------ Original Message ------
Received: Wed, 17 Jun 2009 09:22:42 AM EDT
From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: Makoto Hamana <hamana@cs.gunma-u.ac.jp>, <categories@mta.ca>
Subject: categories: Re: Fundamental Theorem of Category Theory?

> On Mon, 15 Jun 2009, Makoto Hamana wrote:
> 
> > I have asked Prof. Yoneda many years ago why Yoneda Lemma is
> > called "Lemma", not "Theorem". He said that perhaps it was a
> > bit about internal of category theory rather than insisting
> > on applications to other mathematics. Doesn't Yoneda Lemma
> > satisfy (c) in Mile Gould's post? I don't know how much
> > Yoneda Lemma is useful in other areas of mathematics, and
> > I have wanted to know it.
> >
> When I lecture on category theory to first-year graduate students, I
> tell them there are two things they should remember about the
> Yoneda Lemma: it isn't a lemma, and it was never published by Yoneda.
> In this respect it resembles that bulwark of the British constitution,
> the Lord Privy Seal (who is none of the three things that his title
> claims).
> 
> Peter Johnstone
> 



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