Re: Sorry

[Vaughan Pratt <pratt@cs.stanford.edu>]

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Thanks for that "ungated" link to Bénabou's 1985 JSL paper, Wes.

As it turned out, I'd downloaded all 28 pages back in 2011, I can't
remember why.  Moreover it arrived 26 years earlier in my mailbox in 1985,
but who reads every article, especially if you're more on the universal
algebra side than the category theory side in 1985.

Now that it's 2024, what I'm wondering is, is there 28 pages of useful
information there?

I appreciate the idea of a fibration as a functor C → B where B is a "base
category" looking enough like *Set* (aka *Ens*).  In recent years I've been
writing about the Yoneda embedding as a way of viewing Chu spaces over *Set*,
namely as Set-valued functors representing structured objects.  This sort
of thing is closer to toposes than abelian categories, both of which I like
a lot given that the Big Bang seems to have evolved from a topos to (at
least in our neighborhood) an abelian category.

What I'm having difficulty with is why Jean took 28 pages to make his
point.  It seemed better suited to the Journal of Philosophical Logic than
to JSL.

I'm a great fan of Einstein's "make everything as simple as possible but no
simpler".  However that implies that there's a boundary, and in the case of
fibrations and definability, I'm not at all clear as to where that boundary
should be drawn.

Vaughan Pratt
https://protect-au.mimecast.com/s/3wnSC81Vq2CRLlpYinMtKz?domain=clim8.stanford.edu


On Mon, Jan 22, 2024 at 4:03 PM Wesley Phoa <doctorwes@gmail.com> wrote:

> Ungated link to the 1985 JSL paper (see p35 for definition of
> definability):
> https://protect-au.mimecast.com/s/dV7XC91W8rCB9vE2CEg1qQ?domain=artscimedia.case.edu
> <https://protect-au.mimecast.com/s/dV7XC91W8rCB9vE2CEg1qQ?domain=artscimedia.case.edu>
>
>
> Sent
>
> On Jan 22, 2024, at 12:00 PM, Francis Borceux <
> francis.borceux@uclouvain.be> wrote:
>
> 
> Sorry, and thanks to Jon for noticing the slip of terminology in my mail.
>
> Indeed, Bénabou was insisting on the importance of his notion of
> definability.
>
> Francis
>
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