Re: Fundamental Theorem of Category Theory?

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

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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